Question

If 8, 2 are the roots of $x^2+ax+\beta =0$ and 3, 3 are the roots of $x^2+\alpha x+b=0$ , then the roots of $x^2+ax+b=0$ are

• A. 8, - 1
• B. – 9, 2
• C. -8, -2
• D. 9, 1

Answer 1

The correct option is D

9, 1

8, 2 are the roots of $x^2+ax+\beta =0$

$\therefore$ 8 + 2 = 10 = –a, 8.2 = 16 = $\beta$ i.e., a = –10, $\beta$ = 16

3, 3 are the roots of $x^2$ + αx + b = 0

$\therefore$ 3 + 3 = 6 = $-\alpha$, 3.3 = b i.e, $\alpha$ = –6, b = 9

Now, $x^2$ + ax + b = 0 becomes $x^2$ – 10x + 9 = 0

or (x – 1)(x – 9) = 0 $\Rightarrow$ x = 1, 9