First slide

Theory of expressions

Question

The number of real solutions of the equation ${(\frac{9}{10})}^{x} = - 3 + x - x^{2},$ is

Moderate

A

$0$
B

$1$
C

$2$
D

none of these

Solution

Let $f (x) = - 3 + x - x^{2} .$ Then,
$f (x) < 0$ for all $x,$ because coefficient of $x^{2} < 0$ and disc. $< 0 .$
Thus, LHS of the given equation is always positive whereas the RHS is always less than zero. Hence, the given equation has no solution.

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