Question

If the roots of $x^2-ax+b=0$ are two consecutive odd integers, then $a^2-4b$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$
• E. $7$

Answer 1

The correct option is B $4$

Given equation: $x^2-ax+b=0$

Let $\alpha$ and $\beta$ be roots.

It is given that,

$\alpha -\beta =2$ [Roots are two consecutive integers]

$\alpha +\beta =a$ and $\alpha \beta =b$

$\alpha =\frac{a+2}{2}$ and $\beta =\frac{a-2}{2}$

$\Rightarrow \frac{a+2}{2}\times \frac{a-2}{2}=b$

$\Rightarrow a^2-4=4b$

$\Rightarrow a^2-4b=4$

Hence, B is the correct option.