Question

Solve the following quadratic equations by factorisation.

i. 2m(m – 24) = 50 

ii. 25m² = 9

Answer 1

i. 2m (m – 24) = 50 

∴ 2m² – 48m = 50 

∴ 2m² – 48m – 50 = 0 

∴ m² – 24m – 25 = 0 …[Dividing both sides by 2]

∴ m – 25 = 0 or m + 1 = 0 

∴ m = 25 or m = -1

∴ The roots of the given quadratic equation are 25 and -1.

ii. 25m² = 9

∴ 25m² – 9 = 0 

∴ (5m)² – (3)² = 0 

∴ (5m + 3) (5m – 3) = 0 

…. [∵ a² – b² = (a + b) (a – b)]

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

∴ 5m + 3 = 0 or 5m – 3 = 0 

∴ 5m = -3 or 5m = 3

∴ m = -3/5 or m = 3/5

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