https://artofproblemsolving.com/wiki/index.php?title=1958_AHSME_Problems/Problem_33&feed=atom&action=history
1958 AHSME Problems/Problem 33 - Revision history
2024-03-28T13:35:40Z
Revision history for this page on the wiki
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Mathgeek2006: /* Problem */
2015-03-14T03:21:28Z
<p><span dir="auto"><span class="autocomment">Problem</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 03:21, 14 March 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Problem ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Problem ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For one root of <math> ax^2 <del class="diffchange diffchange-inline">\plus{} </del>bx <del class="diffchange diffchange-inline">\plus{} </del>c <del class="diffchange diffchange-inline">\equal{} </del>0</math> to be double the other, the coefficients <math> a,\,b,\,c</math> must be related as follows:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>For one root of <math> ax^2 <ins class="diffchange diffchange-inline">+ </ins>bx <ins class="diffchange diffchange-inline">+ </ins>c <ins class="diffchange diffchange-inline">= </ins>0</math> to be double the other, the coefficients <math> a,\,b,\,c</math> must be related as follows:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math> \textbf{(A)}\ 4b^2 <del class="diffchange diffchange-inline">\equal{} </del>9c\qquad  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math> \textbf{(A)}\ 4b^2 <ins class="diffchange diffchange-inline">= </ins>9c\qquad  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(B)}\ 2b^2 <del class="diffchange diffchange-inline">\equal{} </del>9ac\qquad  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(B)}\ 2b^2 <ins class="diffchange diffchange-inline">= </ins>9ac\qquad  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(C)}\ 2b^2 <del class="diffchange diffchange-inline">\equal{} </del>9a\qquad \\</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(C)}\ 2b^2 <ins class="diffchange diffchange-inline">= </ins>9a\qquad \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(D)}\ b^2 <del class="diffchange diffchange-inline">\minus{} </del>8ac <del class="diffchange diffchange-inline">\equal{} </del>0\qquad  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(D)}\ b^2 <ins class="diffchange diffchange-inline">- </ins>8ac <ins class="diffchange diffchange-inline">= </ins>0\qquad  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(E)}\ 9b^2 <del class="diffchange diffchange-inline">\equal{} </del>2ac</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\textbf{(E)}\ 9b^2 <ins class="diffchange diffchange-inline">= </ins>2ac</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Solution ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Solution ==</div></td></tr>
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Mathgeek2006
https://artofproblemsolving.com/wiki/index.php?title=1958_AHSME_Problems/Problem_33&diff=64276&oldid=prev
Timneh: Created page with "== Problem == For one root of <math> ax^2 \plus{} bx \plus{} c \equal{} 0</math> to be double the other, the coefficients <math> a,\,b,\,c</math> must be related as follows: <ma..."
2014-10-03T10:24:38Z
<p>Created page with "== Problem == For one root of <math> ax^2 \plus{} bx \plus{} c \equal{} 0</math> to be double the other, the coefficients <math> a,\,b,\,c</math> must be related as follows: <ma..."</p>
<p><b>New page</b></p><div>== Problem ==<br />
For one root of <math> ax^2 \plus{} bx \plus{} c \equal{} 0</math> to be double the other, the coefficients <math> a,\,b,\,c</math> must be related as follows:<br />
<br />
<math> \textbf{(A)}\ 4b^2 \equal{} 9c\qquad <br />
\textbf{(B)}\ 2b^2 \equal{} 9ac\qquad <br />
\textbf{(C)}\ 2b^2 \equal{} 9a\qquad \\<br />
\textbf{(D)}\ b^2 \minus{} 8ac \equal{} 0\qquad <br />
\textbf{(E)}\ 9b^2 \equal{} 2ac</math><br />
<br />
== Solution ==<br />
<math>\fbox{}</math><br />
<br />
== See Also ==<br />
<br />
{{AHSME 50p box|year=1958|num-b=32|num-a=34}}<br />
{{MAA Notice}}</div>
Timneh