Question

The polynomial given below has _____ root(s).

2x^2-9x+9

A. two complex
B. two positive
C. one positive and one negative
D. two negative

Answer 1

Since the polynomial is in the 2nd degree, there are two roots. If the discriminant is a perfect square, the roots are real. If not, they are complex.

discriminant = b^2 - 4(a)(c) for the quadratic equation ax^2 + bx + c = 0
discriminant = (-9)^2 - 4(2)(9) = 9 (perfect square)

To know if it is positive or negative, we have to solve the equation:
2x^2 - 9x + 9 = 0
Dividing all terms by 2:
x^2 - 9/2 x + 9/2 = 0
Factoring,
(x - 3)(x - 3/2) = 0
Through zero product property,
x - 3 = 0 => x = 3
x - 3/2 = 0 => x = 3/2

Then, there are two real positive number. The answer is B.