Asked by Ariel
For what values of k will the function f(x)=3x^2-4x+k have on x-interccept
Answers
Answered by
Steve
One intercept means two equal roots.
That means that f(x) = a(x-r)^2
3x^2 - 4x + k = 3(x^2 - 4/3 x + k/3)
= 3(x - -4/3 x + 4/9 + k/3 - 4/9)
= 3(x - 2/3)^2 + 3(k/3 - 4/9)
So, we need k/3 - 4/9 = 0
k = 4/3
3x^2 - 4x + 4/3 = 3(x - 2/3)^2
which has two roots at x = 2/3
That means that f(x) = a(x-r)^2
3x^2 - 4x + k = 3(x^2 - 4/3 x + k/3)
= 3(x - -4/3 x + 4/9 + k/3 - 4/9)
= 3(x - 2/3)^2 + 3(k/3 - 4/9)
So, we need k/3 - 4/9 = 0
k = 4/3
3x^2 - 4x + 4/3 = 3(x - 2/3)^2
which has two roots at x = 2/3
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