Question

If the sum of the roots of a quadratic equation is $2$ and the sum of their cubes is $98$, then find the equation.

• A. $x^2-2x+12=0$
• B. $x^2-2x-15=0$
• C. $x^2-2x+9=0$
• D. $x^2-2x+13=0$

Answer 1

The correct option is B $x^2-2x-15=0$

Let the roots be $\alpha$ and $\beta$. Then,
$\alpha +\beta =2$ and ${\alpha }^3+{\beta }^3=98$
$(\alpha +\beta {)}^3=2^3$

${\alpha }^3+{\beta }^3+3\alpha \times \beta (\alpha +\beta )=8$

$98+3\alpha \beta \left(2\right)=8$

$\alpha \beta =-15$

As we know that $x^2-$(sum of roots) $x+$ product of roots $=0$ is the quadratic equation when sum of roots and product of roots are given.

$\therefore$ the quadratic equation is given as $x^2-2x-15=0$