If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots : (a) show that \(2p^{2} + p - 1 < 0\); (b) find the values...

If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots :

(a) show that \(2p^{2} + p - 1 < 0\);

(b) find the values of p.

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