First slide

Theory of equations

Question

If one of the roots of the equation $x^{2} + ax + b = 0$ and $x^{2} + bx + a = 0$ is coincident, then the numerical value of $(a + b)$ is

Moderate

A

0
B

$- 1$
C

2
D

5

Solution

If $α$ is the coincident root, then $α^{2} + aα + b = 0$ and $α^{2} + bα + a = 0$
$\Rightarrow \frac{α^{2}}{a^{2} - b^{2}} = \frac{α}{b - a} = \frac{1}{b - a} \Rightarrow α^{2} = - (a + b); α = 1 \Rightarrow - (a + b) = 1 \Rightarrow (a + b) = - 1 .$

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