solve the quadratic equation by factorization x²-x-a(a²+1)=0
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Soln:-
Consider, x2 – x –a(a + 1) = 0
⇒ x2 – ax – x + ax – a(a + 1) = 0
⇒ x2 – x(a +1) + ax – a(a + 1) = 0
⇒ x[x – (a +1)] + a[x – (a + 1)] = 0
⇒ [x – (a +1)] [x+ a] = 0
⇒ [x – (a +1)] = 0 or [x+ a] = 0
∴ x = (a +1) or x = –a
Consider, x2 – x –a(a + 1) = 0
⇒ x2 – ax – x + ax – a(a + 1) = 0
⇒ x2 – x(a +1) + ax – a(a + 1) = 0
⇒ x[x – (a +1)] + a[x – (a + 1)] = 0
⇒ [x – (a +1)] [x+ a] = 0
⇒ [x – (a +1)] = 0 or [x+ a] = 0
∴ x = (a +1) or x = –a
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