Question

Find the number of solutions of -x^2 + 5x - 4 = 0.

Answer 1

There are 2 solutions for the equation -x^2 + 5x - 4 = 0 i.e x=1 and x=4

Explanation:

We can find the number of solutions of the given equation -x^2 + 5x - 4 = 0 by solving the equation using factors method to solve the quadratic equation.

`-x^2 + 5x - 4 = 0\\Taking\,\, - sign\,\, common\\x^2 - 5x + 4 = 0\\making\,\, factors\,\, of\,\, 4x^2\\x^2 -4x -x +4 = 0\\x(x -4) -1 (x - 4) = 0\\(x-1)(x-4)=0\\x-1 = 0 \,\, and \,\, x-4 =0\\x = 1 \,\,and\,\, x = 4\\`

The values of x are:

x=1 and x=4

So, there are 2 solutions for the given equation -x^2 + 5x - 4 = 0