CAT 2021 Linear and Quadratic Equations Question (Hard)

Question

If is a constant such that has exactly three distinct real roots, then the value of is

Accepted Answer

Step 1 Let We are solving the equation This equation will have exactly 3 distinct real roots if the line intersects the graph of at 1 point and intersects at 2 points or vice versa . Step 2 Analyze It is a parabola opening upwards. Find its vertex Minimum value of Step 3 Analyze has a minimum value

CAT 2021

Quantitative

Linear and Quadratic Equations

Hard

If $r$ is a constant such that $|x^2 - 4x - 13| = r$ has exactly three distinct real roots, then the value of $r$ is

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