How many real solutions are there to the equation 4x2 plus x 1 equals 0?

Answer 1

If you mean:

4x2 + x - 1 = 0

then:

4x2 + x = 1

x2 + x/4 = 1/4

x2 + x/4 + 1/64 = 17/64

(x + 1/2)2 = 17/64

x + 1/2 = ± √17 / 8

x = (-4 ± √17) / 8

Giving us two real solutions.

If on the other hand you mean:

4x2 + x + 1 = 0

Then:

4x2 + x = -1

x2 + x/4 = -1/4

x2 + x/4 + 1/64 = 15/64

(x + 1/2)2 = 15/64

x + 1/2 = ± √15 / 8

x = (-4 ± √15) / 8

Again, giving us two real solutions.