Question

$\alpha$ and $\beta$ are two numbers such that $\alpha +\beta =6$, $\alpha -\beta =8$. Then, $\alpha$ and $\beta$ are the roots of the quadratic equation __________.

• A. $x^2+6x+7=0$
• B. $x^2-6x-7=0$
• C. $x^2+6x-8=0$
• D. $x^2-6x+8=0$

Answer 1

The correct option is B $x^2-6x-7=0$

Given,$\alpha +\beta =6$ and $\alpha -\beta =8$

$(\alpha +\beta {)}^2=(\alpha -\beta {)}^2+4\alpha \beta$

$\Rightarrow$ $36=64+4\alpha \beta$

$\Rightarrow$ $\alpha \beta =-7$

The quadratic Equation is $x^2-(\alpha +\beta )x+\alpha \beta =0$

$\Rightarrow$ $x^2-6x-7=0$

Therefore, Option B is correct.