Question

Two roots whose sum is $8$ and the absolute value of their difference is $10$, are roots of which of the following equations?

• A. $x^2-8x+9=0$
• B. $x^2-8x-9=0$
• C. $x^2+8x-9=0$
• D. $-(-x^2+8x+9)=0$

Answer 1

Answer: (B), (D)

$x^2-8x-9=0$
$-(-x^2+8x+9)=0$

Let the roots be $\alpha$ and $\beta$
$\alpha +\beta =8,|\alpha -\beta |=10$
$(\alpha -\beta {)}^2=100$

Now, $(\alpha -\beta {)}^2=(\alpha +\beta {)}^2-4\alpha \beta$
$\therefore (\alpha +\beta {)}^2-4\alpha \beta =100$

$\therefore 8^2-4\alpha \beta =100$
$\therefore \alpha \beta =-9$

Hence, the required equation is $x^2-8x-9=0$

or $-(-x^2+8x+9)=0$