CAT 2019 Linear and Quadratic Equations Question (Medium)

Question

Let be a real number. Then the roots of the equation are real and distinct if and only if

Accepted Answer

Step 1 Use Discriminant Condition For a quadratic , the roots are real and distinct if D b 2 - 4ac 0 In this case - - - So, D -4 2 - 4 1 - log_ 2 A 16 4 log_ 2 A We want 16 4 log_ 2 A 0 Rightarrow log_ 2 A -4 --- Step 2 Solve for A log_ 2 A -4 Rightarrow A 2 -4 16 --- Final Answer A 16

CAT 2019

Quantitative

Linear and Quadratic Equations

Medium

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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