Line meets curve

<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the range of values of $p$ such that the equation ${{x}^{2}}-2x-px-\frac{1}{4}p=0$ has real roots.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the range of values of $k$ for which $(1-k){{x}^{2}}+9=4kx$ has real and distinct roots.</span></div></li></ol>

Find the range of values of $p$ such that the equation ${{x}^{2}}-2x-px-\frac{1}{4}p=0$ has real roots.

Find the range of values of $k$ for which $(1-k){{x}^{2}}+9=4kx$ has real and distinct roots.

Question 111684

Question 111684

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