The Discriminant

What types of solutions can a quadratic equation have?

• rational solutions

• irrational solutions

• imaginary solutions

• all of the above

Tags

CCSS.HSA.REI.B.4

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

 $\sqrt{-25}$  is equivalent to

•  $5$  

•  $-5$  

•  $5i$  

•  $-5i$  

Tags

CCSS.HSN.CN.A.1

If the discriminant is a positive perfect square (example: 36), the solutions to the quadratic equation are

• real, rational and unequal

• real, irrational and unequal

• real, rational and equal

• imaginary

Tags

CCSS.HSA.REI.B.4

If the discriminant is a positive nonperfect square (example: 17), the solutions to the quadratic equation are

• real, rational and unequal

• real, irrational and unequal

• real, rational and equal

• imaginary

Tags

CCSS.HSA.REI.B.4

If the discriminant is a negative number (example: -10), the solutions to the quadratic equation are

• real, rational and unequal

• real, irrational and unequal

• real, rational and equal

• imaginary

Tags

CCSS.HSA.REI.B.4

If the discriminant is zero, the solutions to the quadratic equation are

• real, rational and unequal

• real, irrational and unequal

• real, rational and equal

• imaginary

Tags

CCSS.HSA.REI.B.4

If the roots of a quadratic equation are real, irrational and unequal, the discriminant could have a value of

• 1

• 0

• 8

• -6

Tags

CCSS.HSA.REI.B.4

The roots of a quadratic equation are real, rational and equal when the discriminant is

• -2

• 2

• 0

• 4

Tags

CCSS.HSA.REI.B.4

If the graph of a quadratic function lies entirely above or below the x-axis, then the quadratic equation has

• two rational solutions

• two irrational solutions

• exactly one solution

• no real solutions

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

If the graph of a quadratic function is tangent to the x-axis, then the quadratic equation has

• two rational solutions

• two irrational solutions

• exactly one solution

• no real solutions

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4