Question

find the discriminant of the quadratic
x²-10x+5=0 hence write the
nature of the roots​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² - 10x + 5 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

⇒ D = (-10)² - 4(1)(5).

⇒ D = 100 - 20.

⇒ D = 80.

Nature of roots are real and unequal : D > 0.

                                                                                                                       

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.