Question

Solve the equation 2x² + 13x + 15 = 0 by factorisation method, by completing the square method and by using the formula. Verify that you will get the same roots every time.

Answer 1

i. Factorization method :

By using the property, if the product of two numbers is zero, then at least zero, we get 

∴ x + 5 = 0 or 2x + 3 = 0 

∴ x + -5 = 0 or 2x = -3 = 0 

∴ x + -5 = or x = -(3/2) 

∴ The roots of the given quadratic equation are - (3/2)and -5.

ii. Completing the square method: 2x² + 13x + 15 = 0

∴ x = -(3/2) or x = -5

∴ The roots of the given quadratic equation are (-(3/2) and -5.

iii. Formula method: 2x + 13x + 15 = 0 

Comparing the above equation with ax² + bx + c = 0, we get 

a = 2, b = 13, c = 15 

∴ b² – 4ac = (13)² – 4 × 2 × 15 

= 169 – 120 = 49

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

.

∴ The roots of the given quadratic equation -(3/2) are and -5. 

∴ By all the above three methods, we get the same roots of the given quadratic equation.