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# How many real solutions does x 2 -9x+8=0 have? - PowerPoint PPT Presentation

Can you predict whether a quadratic equation will have two real solutions, one real solution, or no real solutions?. How many real solutions does x 2 -9x+8=0 have?.

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Presentation Transcript

Can you predict whether a quadratic equation will have two real solutions, one real solution, or no real solutions?

How many real solutions does x2-9x+8=0 have?

In this lesson you real solutions, one real solution, or no real solutions?will learn how to determine if a quadratic function has two real roots, one real root, or no real roots by looking at the discriminant.

Also called roots real solutions, one real solution, or no real solutions?

0=ax2+bx+c

A quadratic equation can have two solutions.

One way to find them is with the quadratic formula.

Remember to be careful with signs. real solutions, one real solution, or no real solutions?

x2-9x+8=0

is the discriminant

√50= 5√2 , -5√2

Positive number

√0=0

Zero

√-16= 4i, -4i

Negative number

If the discriminant is… roots.

A Positive number

2 DISTINCT real solutions

A graph of the function has

2

DISTINCT x-intercepts

If the discriminant is… roots.

Zero

1 DISTINCT

real solution

A graph of the function has

1

DISTINCT

x-intercept

If the discriminant is… roots.

A negative number

No real solutions

A graph of the function has

no

x-intercepts

x roots.2-9x+8=0

c=8

a=1

b=-9

1

(-9)2 -4(1)(8)

81 – 32 = 49

Discriminant is POSITIVE

We have two distinct real roots.

x2-9x+8

is POSITIVE, the graph of

y=x2-9x+8

shows

two

x-intercepts

In this lesson roots.you learned how to determine if a quadratic function has two real roots, one real root, or no real roots by looking at the discriminant.

What types of roots would a quadratic equation have if your discriminant was -76?

Describe the roots of the quadratic function y=x2-4x+2?