CAT 2022 Question Paper (Slot 3) - Quant Question 2

Question 2

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


$$2x^{2}+kx+5=0$$ has no real roots so D<0

$$k^2-40\ <0$$



$$x^{2}+(k-5)x+1=0$$ has two distinct real roots so D>0




$$k\in\left(-\infty\ ,3\right)∪\left(7,\infty\ \right)$$

Therefore possibe value of k are -6, -5, -4, -3, -2, -1, 0, 1, 2

In 9 total 9 integer values of k are possible.

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