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. Factorisation 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

Comparing the coefficients, we get

Taking square root of both sides, we get

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

iii. Formula method: 

2x² + 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

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

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