Question

x²-4x+4=0 Determine the nature of roots of this quadratic equation.

Answer 1

$\sf{GIVEN:-}$ x² - 4x + 4 = 0

so, we have to find nature of roots
we know if the value if discriminant (D) = 0 (so , roots are real and equal)
if (D) <0(so, roots are imaginary & not equal)
if ( D ) > 0 (so, roots are real but not equal)

so, here in the equation,
x² - 4x + 4 = 0
where, a = 1 , b = -4 , c = 4

D = b² - 4ac

D = (-4)² - 4(1)(4)

D = 16 - 16

D = 0
here, D = 0 so, following the condition roots are real and equal.

Answer 2

Hi ,

Given quadratic equation is

x² - 4x+ 4 = 0

Compare above equation with

ax² + bx + c = 0 , we get

a = 1 , b = -4 , c = 4

Discreaminant ( D ) = b² - 4ac


D = ( -4 )² - 4 × 1 × 4

D = 16 - 16

D = 0

Therefore ,

Roots of the given quadratic equation

Real and equal.

I hope this helps you.

: )