Question

Use the discriminant to describe the roots of each equation. Then select the best description. 6x2 + 13x + 6 = 0. A) Double root B) Real and Rational root C) Real and Irrational D) Non-Real root

Answer 1

Hello!

6x^2 + 13x + 6 has coefficients a = 6, b = 13 and c = 6. The discriminant,

b^2 - 4ac, is therefore 13^2 - 4(6)(6) = 169 - 144 = 25.

Because the discriminant is positive, we have two unequal, real roots. They are:

-13 plus or minus √25

x = -----------------------------------

2(6)

-13 plus or minus 5

= --------------------------------

12

and these come out to -8/12 and -18/12, reductable to -2/3 and -3/2. I'd prefer to state "two real, rational, distinct roots," but "double root" is OK.