SOLUTION: The question is: The quadratic function f is defined by f(x) = {{{4x^2 +5x +2}}} a) Find the set of values of k for which the equation {{{f(x) = kx + 1}}} has real roots.

Algebra ->  Rational-functions -> SOLUTION: The question is: The quadratic function f is defined by f(x) = {{{4x^2 +5x +2}}} a) Find the set of values of k for which the equation {{{f(x) = kx + 1}}} has real roots.       Log On


   



Question 552483: The question is:
The quadratic function f is defined by f(x) = 4x%5E2+%2B5x+%2B2
a) Find the set of values of k for which the equation f%28x%29+=+kx+%2B+1 has real roots.
b) Find the coordinates of the turning point of y+=+f%28x%29, stating whether it is a maximum or a minimum point.
c) Hence, state the maximum value of 1%2F%28f%28x%29%29
Thank you.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic function f is defined by f(x) = 4x%5E2+%2B5x+%2B2
a) Find the set of values of k for which the equation f%28x%29+=+kx+%2B+1 has real roots.
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kx + 1 has real roots for all x ?? How is this related to the quadratic?
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b) Find the coordinates of the turning point of y+=+f%28x%29, stating whether it is a maximum or a minimum point.
The coefficient of the x^2 is >0 --> minimum
The Line of Symmetry is x = -b/2a = -5/8
The min is at (-5/8,f(-5/8))
= (-5/8,-7/16)
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c) Hence, state the maximum value of 1%2F%28f%28x%29%29
For 1/(4x^2 +5x +2)
Max = 2 2/7
Not sure that's what you meant to ask