Sum

Solve (i) x^{2} + 3x – 18 = 0

(ii) (x – 4) (5x + 2) = 0

(iii) 2x^{2} + ax – a2 = 0; where ‘a’ is a real number

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#### Solution

(i) x^{2} + 3x – 18 = 0

⇒ x^{2} + 6x – 3x – 18 = 0

⇒ x(x + 6) – 3(x + 6) = 0

i.e., (x + 6) (x – 3) = 0

⇒ x + 6 = 0 or x – 3 = 0

⇒ x = – 6 or x = 3

Roots of the given equation are – 6 and 3

(ii)(x – 4) (5x + 2) = 0

⇒ x – 4 = 0 or 5x + 2 = 0

x = 4 or x = – 2/5

(iii) 2x^{2} + ax – a^{2} = 0

⇒ 2x^{2} + 2ax – ax – a2 = 0

⇒ 2x(x + a) – a(x + a) = 0

i.e., (x + a) (2x – a) = 0

⇒ x + a = 0 or 2x – a = 0

⇒ x = – a or x = a/2

Concept: Solutions of Quadratic Equations by Factorization

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