1950 AHSME Problems/Problem 3

Problem

The sum of the roots of the equation $4x^{2}+5-8x=0$ is equal to:

$\textbf{(A)}\ 8\qquad\textbf{(B)}\ -5\qquad\textbf{(C)}\ -\frac{5}{4}\qquad\textbf{(D)}\ -2\qquad\textbf{(E)}\ \text{None of these}$

Solution

We can divide by 4 to get: $x^{2}-2x+\dfrac{5}{4}=0.$

The Vieta's formula states that in quadratic equation $ax^2+bx+c$ , the sum of the roots of the equation is $-\frac{b}{a}. Using Vieta's formula, we find that the roots add to$ 2 $or$ \boxed{\textbf{(E)}\ \text{None of these}}$.

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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1950 AHSME Problems/Problem 3

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