Question

Directions:Determine the nature of the roots of the following quadratic equations using the discriminant.

1.)x^2+6x+9=0 discriminant:____ nature of roots:____
2.)x^2+9x+20=0 discriminant:____ nature of roots:____
3.)2x^2-10x+8=0 discriminant:____ nature of roots:____

Answer 1

$\huge{\green{\underline{\underline{Answer:-}}}}$

Solution:

1.) x^2 + 6x + 9 = 0

Comparing with quadratic equation

ax²+ bx + c = 0

Here, a = 1, b = 6, c = 9

Discriminant is denoted by Δ ( Delta) and value of discriminant is b²- 4ac

Δ = b²- 4 ac

Δ = 6²- 4 × 1 × 9

Δ = 36 - 36

Δ = 0

as Δ = 0, so roots of quadratic equation are real and equal

Discriminant = 0

Nature of roots = Real

______________________________________

2.) x^2 + 9x + 20 = 0

Comparing with quadratic equation

ax² + bx + c = 0

Here, a = 1 , b = 9, c = 20

Δ = b²- 4ac

Δ = 9²- 4 × 1 × 20

Δ = 81 - 80

Δ = 1

Δ > 0 (more than zero) hence roots of quadratic equation are real and unequal

Discriminant = 1 or >0

Nature of roots = Real and unequal

______________________________________

3.) 2x^ 2- 10x + 8 = 0

Comparing with quadratic equation

ax² + bx + c = 0

Here, a = 2, b = -10, c = 8

Δ = b²- 4ac

Δ = (-10²) - 4 × 2 × 8

Δ = 100 - 64

Δ = 36

Δ >0 hence roots of the quadratic equation is real and not equal

Discriminant: 36 or more than zero

Nature of roots: Real and unequal

_________________________________

Knowledge booster:

# If the discriminant is negative, it will be less than zero and nature of roots is not real