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


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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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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 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

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.

x2-9x+8=0


The discriminant of a polynomial gives information about its roots.

is the discriminant


We have three different cases when we take square roots.

√50= 5√2 , -5√2

Positive number

√0=0

Zero

√-16= 4i, -4i

Negative number


If the discriminant is…

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…

Zero

The quadratic equation has

1 DISTINCT

real solution

A graph of the function has

1

DISTINCT

x-intercept


If the discriminant is…

A negative number

The quadratic equation has

No real solutions

A graph of the function has

no

x-intercepts


x2-9x+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

x2-9x+8

is POSITIVE, the graph of

y=x2-9x+8

shows

two

x-intercepts


In this lesson 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 type of solutions does a quadratic with a discriminant of 25 have?


  • Draw a rough sketch of a parabola given the following discriminant values.

  • 0, -49, 100, 17


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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