(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The equation kx^{2}- 3x + (k+2) = 0 has two distinct real roots. Find the set of possible values of k.

2. Relevant equations

Since the equation has two distinct real roots, b^{2}- 4ac > 0

3. The attempt at a solution

b^{2}-4ac>0

9-4(k+2)(k)>0

9-4(k^{2}+2k) >0

9-4k^{2}-8k>0

= -4k^{2}-8k+9>0

Multiply both sides by -1,

4k^{2}+8k-9>0

(4k-3)(k+3)>0

-3<k<3/4

However the answer is -2.46<k<0.458

I'm lost, help please!

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# Nature of roots of quadratic equations

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