- #1

- 112

- 5

## Homework Statement

## Homework Equations

Discriminant: b

^{2}- 4ac

## The Attempt at a Solution

a) [/B]f(x) = 3x

^{2}– 5x + 1

y = 3x

^{2}– 5x +1

Substitute a=3, b= -5, c=1 into the discriminant:

b

^{2}– 4ac = (-5)

^{2}– 4(3)(1)

=25 – 12

= 13 This number is positive.

Since b

^{2}– 4ac > 0, there are two real roots, so the quadrative function has two x-intercepts.

**b)**f(x) = 2x

^{2}+ x +1

y = 2x

^{2}+ x +1

Substitute a=2, b=1, c=1 into the discriminant:

b

^{2}– 4ac = (1)

^{2}– 4(2)(1)

= 1 – 8

= -7 This number is negative.

Since b

^{2}– 4ac < 0, there are no real roots, so the quadratic function does not have any x-intercepts.

**c)**f(x) = 4x

^{2}– 12x + 9

y = 4x

^{2}– 12x + 9

Substitute a=4, b= -12, c=9 into the discriminant:

b

^{2}– 4ac = (-12)

^{2}– 4(4)(9)

=144 – 144

= 0

Since b

^{2}– 4ac = 0, there is one (double) real root, so the quadratic function has one x-intercept.

Is this correct?