Question

Find the discriminant and determine how many solutions the equation has and if they are imaginary or real. Please show all work.

y = 4x^2 - 5x + 1

Answer 1

Discriminant = 9 and the equation has two real solutions

Explanation:

For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.

If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.

In this case, y = 4x^2 - 5x + 1.

So its discriminant = -5^2 - 4*4*1

= 9 so it has two real solutions.

Answer 2

as discriminant = 9, it has two real solutions.

Explanation:

for eqn ax^2 + bx + c, discriminant = b^2 - 4ac

y = 4x^2 - 5x + 1

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

= 25 - 16

= 9

as discriminant > 0, it has two real solutions.