Question

Use the discriminant to determine how many and what
kind of solutions the quadratic equation x2 - x = 1/4
has.

Answer 1

Answer:

Step-by-step 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

Answer:

Step-by-step explanation:

x² - x = 1/4

$x^{2}-x -\frac{1}{4}=0\\\\a = 1 \\\\b = -1\\\\c = \frac{-1}{4}\\\\D = b^{2}-4ac\\\\ = (-1)^{2}-4*1*\frac{-1}{4}\\\\= 1 + 1\\= 2$

D = 2 > 0

So, this equation has real roots