SOLUTION: hi can somebody please help me with this question? for what value(s) of k will the function g(x)=x^2+kx+1 have only one zero A.0 B.2 C.-2,2 D. no values will work. Thank you

Question 1090501: hi can somebody please help me with this question?
for what value(s) of k will the function g(x)=x^2+kx+1 have only one zero
A.0
B.2
C.-2,2
D. no values will work.
Thank you so much.
Found 2 solutions by Fombitz, greenestamps:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The quadratic needs to be a perfect square.

So

So then,

and

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

In the quadratic formula, the discriminant, b^2-4ac, tells you whether the quadratic expression has two, one, or no real zeros. If the discriminant is positive, there are two zeros; if it is 0, there is one zero (a double root); if it is negative, there are no real zeros.

So in your example, there is only one zero if the discriminant is zero:

The values -2 and 2 each make the discriminant equal to 0.

So answer C, -2 and 2.
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