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
- Find the range of values of \(p\) such that the equation \({{x}^{2}}-4x-px-\frac{1}{8}p=0\) has real roots.
- Find the range of values of \(k\) for which \(\left( 1-k \right){{x}^{2}}+8=7kx\) has real and distinct roots.
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Answer:(a) \(p\leq\dfrac{-17-\sqrt{33}}4\) or \(p\geq\dfrac{-17+\sqrt{33}}4\) (b) \(k<\dfrac{-16-4\sqrt{114}}{49}\), \(\dfrac{-16+4\sqrt{114}}{49}<k<1\), or \(k>1\)
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