For what values of $a$ is the sum of the roots of the equation $x^{2} + (2 - a - a^{2}) x - a^{2} = 0$ equal to zero?

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Solution

Sum of the roots $= - \frac{(2 - a - a^{2})}{1}$
Sum of roots should be equal to zero
$\Rightarrow - \frac{(2 - a - a^{2})}{1} = 0$
$\Rightarrow (a^{2} + a - 2) = 0$
$\Rightarrow a^{2} + 2 a - a - 2 = 0$
$\Rightarrow a (a + 2) - 1 (a + 2) = 0$
$\Rightarrow (a + 2) (a - 1) = 0$
$\Rightarrow a = - 2, 1$

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For what values of a is the sum of the roots of the equation x2+(2−a−a2)x−a2=0 equal to zero?

Sum of the roots =−(2−a−a2)1Sum of roots should be equal to zero ⇒−(2−a−a2)1=0⇒(a2+a−2)=0⇒a2+2a−a−2=0⇒a(a+2)−1(a+2)=0⇒(a+2)(a−1)=0⇒a=−2,1

For what values of $a$ is the sum of the roots of the equation $x^{2} + (2 - a - a^{2}) x - a^{2} = 0$ equal to zero?