Question

The number of real solutions of the equation `(9/10)^x` = –3 + x – x² is ______.

Options

• 1

• 2

• 0

• 3

Answer 1

The number of real solutions of the equation `(9/10)^x` = –3 + x – x² is 0.

Explanation:

`(9/10)^x` = –(x² – x + 3)

`(9/10)^x` = `{(x - 1/2)^2 + 11/4}`

LHS is always positive while RHS is always negative. Hence LHS ≠ RHS

∴ No real solution