Question

g(x) = 1 - 3x - 9^2

find the discriminant and describe the nature of the solutions.

does this follow into the quadratic formula since there is only one X value?

Answer 1

I assume the last term is -9x^2.

The discriminant = b^2 - 4ac, where a = coefficient of x^2, b = coefficient of x, and c is the constant

Can you find the value of the discriminant?

Answer 2

there is no X after the -9, so could -9 still be used as the A value in this equation?

Answer 3

well, then retype the question's function g(x) again, please. As there seems you left out something somewhere.
@cbhl

Answer 4

g(x) = 1 - 3x - 9^2

The function is presented as so and the I am asked to find the discriminant. C would = 1 and B would = -3 but can we use -9 as A or is there more work that needs to be done here?

Answer 5

A is the coefficient of x^2. But you dont have an x^2 term. Thats why I thought that it said -9x^2. Then there's an error in the problem. But I will assume that they forgot to include the x in -9x^2.

Assuming that I am correct, the discriminant will be equal to what?

Answer 6

the discriminant would be equal to 45, which means there would be two solutions in that case.

Answer 7

Correct. And since 45 is not a perfect square, the two solutions will be real numbers and irrational numbers.

(If the discriminant was 36, then it is a perfect square, and the roots will be real and rational numbers).

Answer 8

A perfect square is something that can be multiplied by itself. 6 * 6 = 36, so 36 would be a perfect square. Sounds right, I guess the instructor forgot an X value in the question, thank you.

Answer 9

Welcome.

(Also, if the discriminant is negative, like -3, then the roots are imaginary (complex) numbers).

Answer 10

Right, cheers.

Answer 11

One final note.

If the discriminant is 0, then the roots are equal and rational.

Answer 12

There would be one solution, in that case.

Answer 13

Yes, that is what's meant by "equal roots".