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

5 x^{2} + 25 x + 165 = 0

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3 x^{2} + 33 x + 165 = 0

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x^{2} + 15 x + 165 = 0

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x^{2} - 38 x + 165 = 0

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Solution

The correct option is D $x^{2} - 38 x + 165 = 0$
In quadratic equations, the product of the roots = constant term. Therefore, the other root is given by,
$5 \times β = 165$
$\Rightarrow β = 33$

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

$∴$ the required quadratic equation is $x^{2} - 38 x + 165 = 0$

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Similar questions

If one of the roots of a quadratic equation is 5 and the product of their roots is -165, then the quadratic equation is :

Write whether the following statemensst are true or false .Justify your answers :

1.Every quadratic equation has at least one real root

2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots .

3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots .

4.A quadratic equation with integeral coeffecient has integral roots.

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