SOLUTION: Find all values of k such that g(x)=3x^2+kx+8 has two distinct real x intercepts. Give the answer in interval notation.

Question 947728: Find all values of k such that g(x)=3x^2+kx+8 has two distinct real x intercepts. Give the answer in interval notation.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is 3x^2 + kx + 8

this is in standard form of ax^2 + bx + c = 0 after you set it equal to 0.

the discriminant can be used to determine the possible values of k.

if the discriminant is greater than or equal to 0, then the roots will be real.

if the discriminant is 0, then there will be only one real root.

if the discriminant is > 0, then there will be 2 distinct real roots.

b^2 - 4ac becomes k^2 - 4*3*8 which becomes k^2 - 96

2 distinct real roots will be when k^2 - 96 > 0

in order to get 2 distinct real roots, then the value of k^2 must be greater than 96.

in interval notation that would be k^2 = (96,infinity)

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