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

Question

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

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Answer

$x^2 - x - a(a + 1) = 0$
$\Rightarrow x^2 + {(a) - (a + 1)}x - a(a + 1) = 0$
${ 1 = a - a + 1}$
$\Rightarrow x^2 + ax - (a + 1)x - a(a + 1) = 0$
$\Rightarrow x(x + a) - (a + 1)(x + a) = 0$
$\Rightarrow (x + a)(x - a - 1) = 0$
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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