Question

The two zeros of the polynomial are always distinct. TRUE FALSE

Answer 1

AnswEr:-

❀ False.

ExplanaTion:-

It is not necessary that in a quadratic polynomial the two roots are always distinct.

Because we know that if the discriminant of any quadratic polynomial is equal to zero then its zeroes must be real and equal.

And if the discriminant is greater than zero then the quadratic polynomial must have real and distinct zeroes.

The Formula of Discriminant(D) Is given below:-

$\\ \tt\longmapsto D = {b}^{2} - 4ac. \\ \\ \rm and \: \: if \\ \tt\longmapsto {b}^{2} - 4ac = 0. \\ \rm then \: \: the \: \: zeroes \: \: must \: \: be \:real \: \: and \: \: equal. \\ \\ \rm also\: if \\ \tt\longmapsto b {}^{2} - 4ac \geqslant 0. \\ \rm then \: \: the \: \: zeroes \: \: must \: \: be \: \: real \: \: and \: \: distinct.$

Where,

• a = Coefficient of x².

• b = Coefficient of x.

• c = Constant Term.