CAT 2022 Linear and Quadratic Equations Question (Hard)

Question

Suppose is any integer such that the equation has no real roots and the equation has two distinct real roots for . Then, the number of possible values of is

Accepted Answer

Step 1 First quadratic equation 2x 2 kx 5 0 Condition No real roots Discriminant k - 5 2 - 4 0 k - 5 2 4 Rightarrow k - 5 2 Rightarrow k - 5 2 k - 5 7 k 7 Rightarrow k 7-66k-6, -5, -4, -3, -2, -1, 0, 1, 2 Count 9 values

CAT 2022

Quantitative

Linear and Quadratic Equations

Hard

Suppose $k$ is any integer such that the equation $2x^2 + kx + 5 = 0$ has no real roots and the equation $x^2 + (k-5)x + 1 = 0$ has two distinct real roots for $x$ . Then, the number of possible values of $k$ is

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