SOLUTION: given the quadratic equation kx^2 - 24x + (k-7) = 0 has real roots, show that a) k^2 - 7k - 144 <= 0 b) find the range of values of k satisfying this inequality

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Question 841314: given the quadratic equation kx^2 - 24x + (k-7) = 0 has real roots, show that
a) k^2 - 7k - 144 <= 0
b) find the range of values of k satisfying this inequality
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is greater than or equal to zero for real roots.
a)D=b%5E2-4ac
D=%28-24%29%5E2-4%28k%29%28k-7%29%3E0
49-4k%5E2%2B28k%3E=0
576-4k%5E2%2B28k%3E=0
-4k%5E2%2B28k%2B576%3E=0
k%5E2-7k-144%3C=0
b)%28k-16%29%28k%2B9%29%3C=0
So the region break points are at k=16 and k=-9
Graph the function and check when it goes below the x-axis (<=0).
graph%28300%2C300%2C-10%2C20%2C-100%2C100%2Cx%5E2-7x-144%29
Values of k : -9%3C=k%3C=16