Question

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

Answer 1

step by step explanation:-

If you have a quadratic equation of the form

ax^2+bx+c=0

The solution is

x=−b±√b^2−4ac2a

The discriminant

Δ

is b2−4ac

.

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

If

Δ>0

, there are two separate real roots.

If

Δ=0

, there are two identical real roots.

If

Δ<0

, there are no real roots, but there are two complex roots.

Your equation is

x2−4x+4=0

Δ=b^2

4ac=(−4)2−4×1×4=16-16=0

This tells you that there are two identical real roots.

We can see this if we solve the equation by factoring.

x2−4x+4=0

(x−2)(x−2)=0

x−2=0 or x−2=0

x=2or x=2

There are two identical real roots to the equation.

I hope my answer is helpful for you ✌️☺️.