Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

TGM Original Questions

Show that the expression \({{x}^{2}}+kx+{{k}^{2}}+k+5\) is always positive for all real values of \(k\).

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Answer:Since \(D\) is always negative and \(a = 1 > 0\), hence \(x^2 + kx + k^2 + k + 5\) is always positive.

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