Question

The roots of the equation $x^2+Ax+B=0$ are 5 and 4. The roots of $x^2+Cx+D=0$ are 2 and 9. Which of the following is a root of $x^2+Ax+D=0$?

• A. 3 & 9
• B. 6 & 3
• C. 6 & 9
• D. 3 & 3

Answer 1

The correct option is B 6 & 3

Let $\alpha ,\beta$ be the roots of $x^2+Ax+B=0$.

So, $\alpha +\beta =-A=9\alpha \beta =B=20$

Let $\gamma ,\delta$ be the roots of $x^2+Cx+D=0$.

So, $\gamma +\delta =-C=11\gamma \delta =D=18$

$x^2+Ax+D=0x^2-9x+18=0x^2-6x-3x+18=0x(x-6)-3(x-6)=0(x-3)(x-6)=0x=3,6$

Hence option B.