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Solve  (i) x^2  + 3x – 18 = 0 (ii) (x – 4) (5x + 2) = 0 (iii) 2x^2 + ax – a^2 = 0; where ‘a’ is a real number - Mathematics

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Sum

Solve  (i) x2  + 3x – 18 = 0

(ii) (x – 4) (5x + 2) = 0

(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number

 

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Solution

(i) x2 + 3x – 18 = 0

⇒ x2 + 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) 2x2 + ax – a2 = 0

⇒ 2x2 + 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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