First slide

Theory of equations

Question

Product of roots of the equation.
$\sqrt{13 - x^{2}} = x + 5$ is

Moderate

A

-6
B

7
C

6
D

-7

Solution

Note that $- \sqrt{13} \leq x \leq \sqrt{13}$ and
$13 - x^{2} = x^{2} + 10 x + 25$
$\Rightarrow x^{2} + 5 x + 6 = 0 \Rightarrow x = - 2, - 3$ .

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