Difference between revisions of "1960 AHSME Problems/Problem 31"
Rockmanex3 (talk | contribs) (Solution to Problem 31) |
Rockmanex3 (talk | contribs) m (→See Also) |
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Substitute <math>c</math> and <math>b</math> back to get | Substitute <math>c</math> and <math>b</math> back to get | ||
<cmath>x^4 + 6x^2 + 25</cmath> | <cmath>x^4 + 6x^2 + 25</cmath> | ||
− | Thus, <math>p=6</math> and <math>q=25</math>, so the answer is <math>\boxed{\textbf{(D)}}</math> | + | Thus, <math>p=6</math> and <math>q=25</math>, so the answer is <math>\boxed{\textbf{(D)}}</math>. |
==See Also== | ==See Also== | ||
{{AHSME 40p box|year=1960|num-b=30|num-a=32}} | {{AHSME 40p box|year=1960|num-b=30|num-a=32}} | ||
+ | |||
+ | [[Category:Intermediate Algebra Problems]] |
Latest revision as of 19:15, 17 May 2018
Problem
For to be a factor of
, the values of
and
must be, respectively:
Solution
Let the other quadratic be , where
. Multiply the two quadratics to get
Since
have no
term and no
term, the coefficients of these terms must be zero.
Substitute
and
back to get
Thus,
and
, so the answer is
.
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 30 |
Followed by Problem 32 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |