# Functions:using discriminant to find number of x-intercepts

1. May 21, 2016

### Evangeline101

1. The problem statement, all variables and given/known data

2. Relevant equations
Discriminant: b2 - 4ac

3. The attempt at a solution
a)
f(x) = 3x2 – 5x + 1

y = 3x2 – 5x +1

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

b2 – 4ac = (-5)2 – 4(3)(1)

=25 – 12

= 13 This number is positive.

Since b2 – 4ac > 0, there are two real roots, so the quadrative function has two x-intercepts.

b) f(x) = 2x2 + x +1

y = 2x2 + x +1

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

b2 – 4ac = (1)2 – 4(2)(1)

= 1 – 8

= -7 This number is negative.

Since b2 – 4ac < 0, there are no real roots, so the quadratic function does not have any x-intercepts.

c) f(x) = 4x2 – 12x + 9

y = 4x2 – 12x + 9

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

b2 – 4ac = (-12)2 – 4(4)(9)

=144 – 144

= 0

Since b2 – 4ac = 0, there is one (double) real root, so the quadratic function has one x-intercept.

Is this correct?

2. May 21, 2016

### Mastermind01

This is absolutely correct. You can additionally verify by drawing the graphs for the equations.

3. May 21, 2016

### Evangeline101

Okay. Thanks for verifying my answer

4. May 21, 2016

### Mastermind01

You are welcome. However you could have done it yourself by hand-drawing the graph or using a graphing calculator.

5. May 21, 2016

### Evangeline101

Oh okay. But this is the way they taught me in the lesson, they did not ask me to graph anything.

6. May 21, 2016

### Mastermind01

7. May 21, 2016

### Evangeline101

Oh okay, I get it :)
Thanks again for the help.