Question

Given the trinomial 2x*2 + 4x + 4, predict the type of solutions.
a. Two rational solutions
b. One rational solution
c. Two irrational solutions
d. Two complex solutions

Answer 1

Can you clarify the terminllogies

Answer 2

What's your aim here?

Answer 3

The form of the roots of a quadratic expression is identified by the discriminant.

The discriminant of the quadratic ax² + bx + c is:
D = b² - 4ac

If D ≥ 0, there are two real valued roots.
If D = 0, there are two real, equal, rational which are sometimes erroneously interpreted as a single rational root.
If D > 0 and is a perfect square, there are two real, unequal, and rational roots.
If D > 0 and is not a perfect square, there are two real, unequal, and irrational roots.
if D < 0, there are two complex valued solutions which form a complex conjugate pair.

In this case, the quadratic is 2x² + 4x + 4, and the determinate is:
D = 4² - 4(2)(4) = 16 -32 = -16

Since the determinate is less than zero, the form of the roots is a conjugate pair of complex roots or two complex roots

Answer 4

OKAY YOU KNOW WHAT!

Answer 5

2 complex solution.

b^2 - 4ac >0

Answer 6

c:

Answer 7

d. Two complex solutions