Use the discriminant to describe the roots of each equation. then select the best description. 7x2 + 1 = 5x

Hello from MrBillDoesMath!

The quadratic has NO real roots. Both roots are imaginary.

Discussion:

I believe the equation involved is  7x^2 + 1 = 5x.

7x^2 + 1 = 5x      => subtract 5x from both sides

7x^2 -5x + 1 = 0

Discriminant of ax^2 + bx + c = 0 is b^2 - 4ac. In our case it is

(-5)^2 - 4 (7) (1) =

25 - 28 =

-3.

Since it is negative the quadratic has NO real roots. Both roots are imaginary.

The solutions are x = 1/14 (5 +\- i sqrt(3))

Thank you,

MrB

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions