Question

Use the discriminant to determine how many and what

kind of solutions the quadratic equation x2 - x = 1/4
has.

Answer 1

Explanation:

x²-x-1/4=0

or 4x²-4x-1=0

disc.=(-4)²-4(4)(-1)=16+16=32>0 ,not a perfect square.

Roots are real,different and irrational.

It has 2 roots or 2 solutions.

Answer 2

Explanation:

x² - x = 1/4

`x^(2)-x -(1)/(4)=0\\\\a = 1 \\\\b = -1\\\\c = (-1)/(4)\\\\D = b^(2)-4ac\\\\ = (-1)^(2)-4*1*(-1)/(4)\\\\= 1 + 1\\= 2`

D = 2 > 0

So, this equation has real roots