Question

3. Determine the nature of roots of the following quadratic equations.
x²-4x+4=0​

Answer 1

Answer:

x

2

−4x+4=0

Comparing the given equation with the quadratic equation ax

2

+bx+c=0

a=1,b=−4 and c=4

Discriminant,

Δ=b

2

−4ac=(−4)

2

−4×1×4=16−16=0

Since the discriminant =0

so, the roots of the given quadratic equation are real and equal.

Answer 2

Given:

• Equation → x² - 4x + 4

To find:

Nature of roots = ?

Formula used:

$\rm{For \: finding\:the\:nature\:of\:roots,}\\\\\bf{D = b^{2} - 4ac}\\\\\tt{where,}\\\\\star \quad \sf{D=Discriminant}\\\star \quad \sf{a = 1}\\\star \quad \sf{b = -4}\\\star \quad \sf{c=4}$

D = b² - 4ac

⇒ D = (-4)² - 4(1)(4)

⇒ D = 16 - 16

∴ D = 0

Since D = 0, the given quadratic equation has 1 real and equal root.

Additional Information:

1. If D > 0, the equation will have 2 real and distinct roots.
2. If D < 0 , the equation will have 2 non real or imaginary roots.