First slide

Theory of equations

Question

Solution set of
$\sqrt{3 - x} = - x^{2} - x - 1, x \in R$ is

Moderate

A

$(- 1, \infty)$
B

(0,1)
C

$(- 1, 3 / 4)$
D

$ϕ$

Solution

Note that LHS $= \sqrt{3 - x} \geq 0 \forall x \leq 3$ .
and RHS = $= - {(x - \frac{1}{2})}^{2} - \frac{5}{4} < 0 \forall x$
Thus, the given equation has no solution.

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