Question

If 2x^2+5x-12=(2x-3)(x+4) which equations should be solved to find the roots of 2x^2+5x-12=0

Answer 1

Answer:

The equation should be solved to find the roots of 2x² + 5x - 12 = 0 is

(2x - 3)(x + 4) = 0

Step-by-step explanation:

The roots of an equation is values of x when y is equal to zero

∵ y = 2x² + 5x - 12 is a quadratic equation

∴ The roots of the equations are values of x when y = 0

∵ The factorization of 2x² + 5x - 12 is (2x - 3)(x + 4)

∵ 2x² + 5x - 12 = (2x - 3)(x + 4)

∵ 2x² + 5x - 12 = 0

- Equate the right hand side above by 0

∴ (2x - 3)(x + 4) = 0

- Now equate each bracket by 0 to find the values of x

∵ 2x - 3 = 0

- Add 3 to both sides

∴ 2x = 3

- Divide both sides by 2

∴ x = 1.5

∵ x + 4 = 0

- Subtract 4 from both sides

∴ x = -4

∴ The roots of the equations are -4 and 1.5

The equation should be solved to find the roots of 2x² + 5x - 12 = 0 is

(2x - 3)(x + 4) = 0