Question

The number of real solutions of the equation
${\left(\frac{7}{10}\right)}^x=-4+3x-x^2$ is

• A. Only one
• B. Only two
• C. Atleast one
• D. No solution

Answer 1

The correct option is D No solution

${\left(\frac{7}{10}\right)}^x=-4+3x-x^2$
$\Rightarrow {\left(\frac{7}{10}\right)}^x=-[x^2-3x+4]$
$\Rightarrow {\left(\frac{7}{10}\right)}^x=-[{(x-\frac{3}{2})}^2+\frac{7}{4}]$
L.H.S is always $>0$ but RHS is $<0$ for all values of $x$. hence equation has no solution.