Question

For quadratic equation 9x^2-12x+4=0 find b^2-4ac

Answer 1

Answer:

On comparing 9x^2 - 12 x + 4 = 0 with ax^2 + bx + c = 0, we get :

a = 9 , b = - 12 , c = 4

Therefore, discriminant = b^2 - 4ac

= ( - 12 )^2 - 4( 9 × 4 )

= 144 - 144

= 0

Discriminant = 0

Applying quadratic formula,

x = \dfrac{-b \pm \sqrt{discriminant}}{2a}

2a

−b±

discriminant

x = \dfrac{- ( - 12 ) \pm \sqrt{0}}{2( 9 ) }

2(9)

−(−12)±

0

x = \dfrac{ + 12 }{2( 9 )}

2(9)

+12

x = \dfrac{2}{3}

3

2

As discriminant was 0, roots are real and equal. therefore roots are 2 / 3 and 2 / 3.

Answer 2

Answer:

b² - 4ac = 0

Step-by-step explanation:

(a ± b)² = a² ± 2ab + b²

ax² + bx + c = 0

D = b² - 4ac ≥ 0

~~~~~~~~~

9x² - 12x + 4 = 0

D = (- 12)² - 4(9)(4) = 144 - 144 = 0 ⇒ quadratic equation has only one root.

(3x)² - 2(3x)(2) + 2² = 0

(3x - 2)² = 0 ⇒ x = 2/3