Solve the following quadratic equations by factorization: x^2-x-a… - Vidyadip

Question

Solve the following quadratic equations by factorization:
$x^2-x-a(a+1)=0$

✓

Answer

$x^2-x-a(a+1)=0$
$⇒ x^2+ {(a) - (a + 1)}x - a(a + 1) = 0$
${ 1 = a - a + 1}$
$⇒ x^2+ ax - (a + 1)x - a(a + 1) = 0$
$⇒ x(x + a) - (a + 1)(x + a) = 0$
$⇒ (x + a)(x - a - 1) = 0$
Either $x + a = 0,$ then $x = -a$
or $x - a - 1 = 0,$ then $x = a + 1$
$\therefore$ Roots are $-a, a + 1$

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