Find the range of values of $\displaystyle k$ if $\displaystyle kx^2 + 8x > 6 - k$ for all real values of $\displaystyle x$.

The answer given is k > 8.

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- Apr 8th 2011, 07:10 AMIlsaQuadratic Inequality
Find the range of values of $\displaystyle k$ if $\displaystyle kx^2 + 8x > 6 - k$ for all real values of $\displaystyle x$.

The answer given is k > 8. - Apr 8th 2011, 07:58 AMSambit
Find its discriminant and solve the equation

**discriminant=0**for k; then take a value of k which (i) is smaller than the smaller root, (ii) is higher than the higher root and (iii) lies between the two roots. Take that region which satisfies the equation you mentioned. - Apr 8th 2011, 08:23 AMIlsa
I am getting the answer as k > -2 or k > 8. Why is only k > 8 specified in the answer?

- Apr 8th 2011, 09:27 AMHallsofIvy
You have two errors: you get x> 2 (not -2)

**and**x> 8 (not or). In order that**both**of those be true, x must be greater than 8.