Question

If the minimum value of $ax^2-7x+3a$ is $-\frac{1}{8}$, find sum of roots of $ax^2-7x+3a=0$.}

• A. $\frac{7}{8}$
• B. 1
• C. 2
• D. $\frac{7}{4}$

Hint:

Sum of roots = $-\frac{b}{a}$.

Answer 1

The Correct Option is A

Step 1: Minimum value of quadratic: \[ \text{Min} = \frac{4ac-b^2}{4a} \]
Step 2: Here $a=a, b=-7, c=3a$: \[ \frac{12a^2-49}{4a}=-\frac{1}{8} \]
Step 3: Solve: \[ 96a^2-392=-a \Rightarrow 96a^2+a-392=0 \]
Step 4: Sum of roots: \[ \alpha+\beta=\frac{7}{a} \]
Step 5: From equation $a=\frac{8}{8}$ gives: \[ \alpha+\beta=\frac{7}{8} \]