Question

Solve the following quadratic equations by factorisation.

i. x² – 15x + 54 = 0 

ii. x² + x – 20 = 0 

iii. 2y² + 27y + 13 = 0 

Answer 1

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

∴ x – 9 = 0 or x – 6 = 0 

∴ x = 9 or x = 6 

∴ The roots of the given quadratic equation are 9 and 6.

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

∴ x + 5 = 0 or x – 4 = 0 

∴ x = -5 or x = 4

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

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

∴ y + 13 = 0 or 2y + 1 = 0 

∴ y = – 13 or 2y = -1 

∴ y = -13 or y = –\(\frac{1}{2}\)

∴ The roots of the given quadratic equation are -13 and – \(\frac{1}{2}\)