Roots of quadratic equation 2x2 – x – 6 = 0 are (A) -2, 3/2(B) 2

1.	Roots of quadratic equation 2x2 – x – 6 = 0 are (A) -2, 3/2(B) 2, -3/2(C) -2, -3/2(D) 2, 3/2
Answer» Answer is (B) 2, - 3/2 Given quadratic equation is : 2x² – x – 6 = 0 ⇒ 2x² – (4 – 3) x – 6 = 0 ⇒ 2x² – 4x + 3x – 6 = 0 ⇒ (2x² – 4x) + (3x – 6) = 0 ⇒ 2x(x – 2) + 3(x – 2) = 0 ⇒ (x – 2)(2x + 3) = 0 ⇒ x-2 = 0 or 2x + 3 = 0 ⇒ x = 2 or x = -3/2

Roots of quadratic equation 2x2 – x – 6 = 0 are (A) -2, 3/2(B) 2, -3/2(C) -2, -3/2(D) 2, 3/2

Answer»

Answer is (B) 2, - 3/2

Given quadratic equation is :

2x² – x – 6 = 0

⇒ 2x² – (4 – 3) x – 6 = 0

⇒ 2x² – 4x + 3x – 6 = 0

⇒ (2x² – 4x) + (3x – 6) = 0

⇒ 2x(x – 2) + 3(x – 2) = 0

⇒ (x – 2)(2x + 3) = 0

⇒ x-2 = 0 or 2x + 3 = 0

⇒ x = 2 or x = -3/2