Question

The equation, pi^x= - 2x2 + 6x - 9 has:
(1) no solution
(2) one solution
(3) two solutions
(4) infinite solutions

Answer 1

Let's focus on each function on each hand.

• $\pi ^x$ is an exponential function.

• $-2x^2+6x-9$ is a quadratic function.

 

The range of the first function is $\pi ^x>0$.

But, $-2x^2+6x-9$ has a negative discriminant, which is $D=-36$.

The quadratic function does not meet the y-axis under it, hence it never crosses against $\pi ^x$, which is above the y-axis.

No point of intersection, hence no solutions.

 

More information:

This form of equations is not solvable algebraically. It is able to solve this analytically, which is using a graph.

Answer 2

Question= The equation, pi^x= - 2x2 + 6x - 9 has:

(1) no solution

(2) one solution

(3) two solutions

(4) infinite solutions

Solution ⬇️

−2x² +6x−9=−x²- −(x² −6x+9)

=−x² −(x−3)²

And π <0 ∀x

So, the equation −2x² +6x−9=π has no solution

So, the answer is option (A)