Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.

"Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.

0 = 2x^2 – 7x – 9

0 = 4x^ 2 – 3x – 1

The quadratic equations that have real number solutions are; 4x^2 – 3x – 1, and 2x^2 – 7x – 9.

What is the formula for Discriminant?

The formula for finding the discriminant is

[tex]b^2 - 4ac[/tex]

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

For the quadratic equation [tex]2x^2 - 7x - 9[/tex]

[tex]b^2 - 4ac[/tex]

[tex]= (-7) ^2 - 4( 2) ( -9)\\\\= 49 + 72 = 121[/tex]

This equation has two real number solutions.

For the quadratic equation [tex]4x^ 2 - 3x- 1[/tex]

[tex]b^2 - 4ac[/tex]

[tex]= (-3) ^2 - 4( 4) ( -1)\\\\= 9 + 16 = 25[/tex]

This equation will have two real number solutions.

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