Question

solve by factorization method​

Answer 1

Answer:

The roots of the given quadratic equation are x = - 5 and x = 4.

Step-by-step-explanation:

The given quadratic equation is

x² + x - 20 = 0.

We have to find 2 factors of 20x² such that their difference is 1x.

Factors of 20x²:

• 1x & 20x

Difference = 20x - 1x = 19x

• 2x & 10x

Difference = 10x - 2x = 8x

• 4x & 5x

Difference = 5x - 4x = 1x

So, to split the middle term of the equation, the required factors are 5x and 4x.

∴ x² + x - 20 = 0 becomes

⇒ x² + 5x - 4x - 20 = 0

⇒ x ( x + 5 ) - 4 ( x + 5 ) = 0

⇒ ( x + 5 ) ( x - 4 ) = 0

⇒ ( x + 5 ) = 0 OR ( x - 4 ) = 0

⇒ x + 5 = 0 OR x - 4 = 0

⇒ x = - 5 OR x = 4

∴ The roots of the given quadratic equation are x = - 5 and x = 4.