Question

Two real numbers $\alpha \& \beta$ are such that $\alpha+\beta=3$ and difference of $\alpha$ and $\beta$ is 4 , then $\alpha \& \beta$ are the monts of the quadratic equation:

• A. $4 x^2-12 x-7=0$
• B. $4 x^2-12 x+7=0$
• C. $4 x^2-12 x+25=0$
• D. $4 x^2+12 x+7=0$

Answer 1

Answer: (A)

$|\alpha-\beta|=4 $
$\Rightarrow (\alpha-\beta)^2=16 $
$\Rightarrow (\alpha+\beta)^2-4 \alpha \beta=16$
$\Rightarrow 9-4 \alpha \beta=16 $
$\Rightarrow \alpha \beta=-7 / 4$
$\Rightarrow $ equation is $x^2-3 x-\frac{7}{4}=0$