Question

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be:

• A. $x^2–5x+10=0$
• B. $x^2+5x–5=0$
• C. $x^2–5x+5=0$
• D. $x^2+10x+5=0$

Answer 1

The correct option is C

$x^2–5x+5=0$

For a quadratic equation $a{x}^2+bx+c=0$,

sum of roots = $-\frac{b}{a}$

product of roots = $\frac{c}{a}$.

sum of roots = 5 = $-\frac{b}{a}$

product of roots = 5 = $\frac{c}{a}$,

Thus, quadratic equation is $x^2-5x+5=0$.

or

A quadratic equation with roots $\alpha$ and $\beta$ is of the form $x^2-(\alpha +\beta )x+\alpha \ast \beta =0$,

sum of roots = 5 = $\alpha +\beta$;

product of roots = 5 = $\alpha \ast \beta$;

so the required equation is $x^2-5x+5=0$.