Let A be a real number. Then the roots of the equation x 2 - 4x - log 2 A = 0 are real and distinct if and only if

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A > 1/16 — Easy A quadratic has real, distinct roots exactly when its discriminant is strictly positive. Set up $D>0$ for the given equation and solve the resulting logarithmic inequality for $A$. 1 Write the discriminant. For $x^{2}-4x-\log_{2}A=0$ we have $a=1,\ b=-4,\ c=-\log_{2}A$. $$\begin{aligned} &D=b^{2}-4ac\ &\Rightarrow\ D=(-4)^{2}-4(1)(-\log_{2}A) \quad	ext{(substitute coefficients)}\ &\Rightarrow\ D=16+4\log_{2}A \end{aligned}$$ 2 Impose $D>0$. Real and distinct roots require a strictly posi

CAT 2019 Slot 2 — QA Question 13

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