How do you use the discriminant to find the number of real solutions of the following quadratic equation: 2x²+4x+2=0.

Solution:

Roots of the quadratic equation of the form ax²+bx+c=0 are given by the expression:

[-b ± √b² - 4ac]/2a

Hence the roots of the given equation are:

b = 4; a = 2; c = 2

The root(s) are = - 4 ± √(4)² - 4(2)(2) = - 4 ± √16 - 16 = -4 ± √0 = -1

Since the discriminant b² - 4ac is equal to zero, it implies the quadratic equation has two equal real and rational roots.

How do you use the discriminant to find the number of real solutions of the following quadratic equation: 2x²+4x+2=0.

Summary:

The discriminant (b² - 4ac) value is zero hence roots are real and equal