Question

If x² - 4x + 4b = 0 has two real solutions, find the value of 'b'.​

Answer 1

Answer:

The required value of b is either 1 or lesser than 1.

Step-by-step explanation:

Given,

x^2 - 4x + 4b = 0 has two real solutions. So the discriminant must equal or greater than 0.

On comparing the given equation with ax^2 + bx + c = 0 { variables used in this equation are different from the variables given in question }.

a = 1 ; b = - 4 ; c = 4b

= > Discriminant of x^2 - 4x + 4b = ( - 4 )^2 - 4( 1 × 4b ) ≥ 0 { b^2 - 4ac is the discriminant of equation ax^2 + bx + c = 0 }

= > Discriminant of x^2 - 4x + 4b = 16 - 4( 4b ) ≥ 0 = > 16 - 16b ≥ 0 = > 16 ≥ 16b = > 1 ≥ b

Thus,

The required value of b is either 1 or lesser than 1.