First slide

Theory of equations

Question

If $α, β$ are the roots of $x^{2} + b x + c = 0$ and $α + h, β + h$ are the roots of $x^{2} + q x + r = 0$ then, $h$

Moderate

A

$b + q$
B

$b - q$
C

$\frac{b + q}{2}$
D

$\frac{b - q}{2}$

Solution

From the given equations, we obtain
$α + β = - b$ and $(α + h) + (β + h) = - q$
$\Rightarrow α + β = - b$ and $α + β + 2 h = - q$
$\Rightarrow - b + 2 h = - q \Rightarrow h = \frac{b - q}{2}$

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