1955 AHSME Problems/Problem 32

Problem 32

If the discriminant of $ax^2+2bx+c=0$ is zero, then another true statement about $a, b$ , and $c$ is that:

$\textbf{(A)}\ \text{they form an arithmetic progression}\\ \textbf{(B)}\ \text{they form a geometric progression}\\ \textbf{(C)}\ \text{they are unequal}\\ \textbf{(D)}\ \text{they are all negative numbers}\\ \textbf{(E)}\ \text{only b is negative and a and c are positive}$

Solution

The discriminant of a quadratic is

$\Delta = b^2 - 4ac = (2b)^2 - 4ac = 4b^2 - 4ac = 0.$ We know that $b^2 = ac,$ or $\frac{b}{a} = \frac{c}{b}$ so $a, b, c$ form a geometric progression.

$\boxed{\text{(B)}}$

1955 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 31	Followed by Problem 33
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1955 AHSME Problems/Problem 32

Problem 32

Solution

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