Question

Can someone help check my answers please? I'm really confuseddd
1. To open these doors, you must match the number and type of solutions for the following two functions in standard form.
• f(x) = x^2 + 6x – 16
• g(x) = x^2 + 6x + 1
Match the following descriptions of the solutions to each of the functions above.
Hint: they each have their own match.
• Two real irrationals solutions.
• Two real rational solutions.

I got -28 and irrational for f(x) and 32 and rational for g(x).

Answer 1

F(x) has 2 real roots -> y = (x -2)(x + 8)
g(x) has 2 real roots -> y = [x -(-3 + V2][x - (-3 - V2)]
the 2 real roots are: (-3 + V2) , and (-3 - V2)
I don't understand what you means: -28 and irrational for f(x)?

Answer 2

i'm supposed to be using the discriminate formula b^2 - 4ac, right?

Answer 3

For f(x) you can factor directly, using the factoring AC method (You Tube)
For g(x) you must find the Discriminant D = b^2 - 4ac.
D = 36 - 4 = 32 = 16*2 --> D = 4V2
x1 = -6/2 + 4V2/2 = -3 + 2V2, and x2 = -3 - 2V2

Answer 4

Correction: The 2 real roots of g(x) are x1 = -3 + 2V2, and
x= -3 - 2V2.
In factoring form: g(x) = [x - (-3 + 2V2)]{x - (-3 - 2V2)] = 0