Discriminant Warmup

The discriminant is

• aX²  + bX  +  c

• b - 4ac

• b² - 4ac

• b² + 4ac

Answer explanation

The discriminant of a quadratic equation ax² + bx + c is given by the formula b² - 4ac. This value helps determine the nature of the roots of the equation. Therefore, the correct answer is b² - 4ac.

Tags

CCSS.HSA-REI.B.4B

If the discriminant is positive, then the solution will be

• one real solution

• two real solutions

• no real solutions

• one imaginary solution

Answer explanation

If the discriminant is positive, it indicates that there are two distinct real solutions to the quadratic equation. Therefore, the correct answer is 'two real solutions'.

Tags

CCSS.HSA-REI.B.4B

A function has a discriminant of 25.
______________
How many solutions does it have?

• 0

• 1

• 2

• 5

Answer explanation

A discriminant of 25 indicates that the quadratic equation has two distinct real solutions, as it is positive. Therefore, the correct answer is 2.

Tags

CCSS.HSA-REI.B.4B

The roots of a quadratic equation are real and equal, then the discriminant is ____.

• 
  Zero

• Positive and a perfect square

• Positive but not a perfect square

• Negative

Answer explanation

The discriminant of a quadratic equation is given by b² - 4ac. When the roots are real and equal, the discriminant equals zero, indicating a perfect square. Thus, the correct answer is 'Zero'.

Tags

CCSS.HSA-REI.B.4B

If the discriminant is equal to 400, the nature of roots of the quadratic equation is ____.

• 
  real and equal

• rational and unequal

• irrational and unequal

• no real roots

Answer explanation

The discriminant (D) of a quadratic equation determines the nature of its roots. A D of 400 is positive and a perfect square, indicating two distinct rational roots. Thus, the correct choice is 'rational and unequal'.

Tags

CCSS.HSA-REI.B.4B

If the discriminant is equal to -7, the nature of roots of quadratic equation is ____.

• 
  real and equal

• rational and unequal

• irrational and unequal

• no real roots

Answer explanation

The discriminant (D) of a quadratic equation determines the nature of its roots. A negative discriminant, like -7, indicates that there are no real roots, only complex roots. Thus, the correct choice is 'no real roots'.

Tags

CCSS.HSA-REI.B.4B