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  4. The equation, πx=-2 x2+6 x-9 has:

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Q. The equation, $\pi^x=-2 x^2+6 x-9$ has:

Complex Numbers and Quadratic Equations

Solution:

$\pi^x=-2 x^2+6 x-9$
RHS $=-2 x^2+6 x-9$
$D=36-4(-9)(-2)=36-72<0$
$-36< 0$
RHS is always negative for all values of $x$ but LHS is positive always so no solution