Question

If one of the roots of a quadratic equation is 5 and its constant term is 165. Then the quadratic equation is :

• A. $5x^2+25x+165=0$
• B. $3x^2+33x+165=0$
• C. $x^2+15x+165=0$
• D. $x^2-38x+165=0$

Answer 1

The correct option is D $x^2-38x+165=0$

In quadratic equations, the product of the roots = constant term. Therefore, the other root is given by,
$5\times \beta =165$
$\Rightarrow \beta =33$

The roots of the equation are 5, 33

Sum of roots = 5 + 33 = 38

- (Sum of roots) = coefficient of $x$ in a quadratic equation = - 38

$\therefore$ the required quadratic equation is $x^2-38x+165=0$