Question

Use the discriminant to describe the roots of each equation. Then select the best description.

7x2 + 3 = 8x



double root

real and rational root

real and irrational root

imaginary root

Answer 1

The Discriminant:
The expression in the square root, D = b^2 - 4ac , is called the discriminant, because its value can be used to discriminate between the different types of solutions that are possible:

1) D > 0 results in two real solutions:
a) If D is a perfect square (like 4, 9 64, 100, etc.) then you get two rational solutions.
b) If D is a not perfect square then you get two irrational solutions.

2) If D = 0 then you get a single real (and rational since 0 is a perfect square) solution.

3) If D < 0 then you get two complex solutions. (Note: you only get imaginary solutions if the discriminant is negative and b = 0!)