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

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?

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