Nature of roots, sum and product of roots

2x² + 5x - 1 = 0
What is the nature of the roots?

• Two unequal real roots
• Two equal real roots
• No real roots

y = -x² + 8x - 16
How many x-intercepts are there?

• 0
• 1
• 2

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

4x² - 7x + 4 = 0
What is the nature of the roots?

• 2 distinct real roots
• Repeated real roots
• Two unreal roots 

y = (-1/2)x² - 3x + 2
How many x-intercepts are there?

• 2
• 1
• 0

y = x² - 4x + (3 + p) has two x-intercepts.
What is the range of values of p?

• p > 1
• p < 1
• p ≥ 1
• p ≤ 1

y = (1 - p)x² + 6x - 5 does not intersect the x-axis.
What is the range of values of p?

• p > 14/5
• p < 14/5
• p > - 14/5
• p < - 14/5

The quadratic equation 4x² + 8x - (2p - 1) = 0 has real roots.
What is the range of values of p?

• p > -3/2
• p < -3/2
• p ≥ -3/2
• p ≤ -3/2

2x² - 6x - 7 = 0
What are the sum and the product of roots?

• Sum = 3
  Product = 7/2
• Sum = - 3
  Product = - 7/2
• Sum = - 3
  Product = 7/2
• Sum = 3
  Product = - 7/2

-2x² - 5x + 1 = 0
What are the sum and product of roots?

• Sum = 5/2
  Product = 1/2
• Sum = - 5/2
  Product = - 1/2
• Sum = - 5/2
  Product = 1/2
• Sum = 5/2
  Product = - 1/2

ax² - 3x - c = 0
Given the sum and product of roots are 6 and -9 respectively. What are the values of a and c?

• a = 1/2
  c = 9/2
• a = - 1/2
  c = - 9/2
• a = - 1/2
  c = 9/2
• a = 1/2
  c = - 9/2