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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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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?

Quadratic equation

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



We have three different cases when we take square roots. roots.

√50= 5√2 , -5√2

Positive number

√0=0

Zero

√-16= 4i, -4i

Negative number


If the discriminant is… roots.

A Positive number

The quadratic equation has

2 DISTINCT real solutions

A graph of the function has

2

DISTINCT x-intercepts


If the discriminant is… roots.

Zero

The quadratic equation has

1 DISTINCT

real solution

A graph of the function has

1

DISTINCT

x-intercept


If the discriminant is… roots.

A negative number

The quadratic equation has

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.


Since the discriminant of 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?


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