CAT 2022 Slot 3 QA Question 22: 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 o

Question

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 o

Accepted Answer

For a quadratic equation to have no real roots, its discriminant must be negative.
$k^2 - 4 	imes 2 	imes 5 
$k^2 
Since $k$ is an integer,
$-6 \leq k \leq 6$
For the second equation to have two distinct real roots, its discriminant must be positive.
$(k - 5)^2 - 4 > 0$
$(k - 5)^2 > 4$
So $k - 5$

Suppose k is any integer such that the equation 2x2+kx+5=02x^2 + kx + 5 = 02x2+kx+5=0 has no real roots and the equation x2+(k−5)x+1=0x^2 + (k - 5)x + 1 = 0x2+(k−5)x+1=0 has two distinct real roots for x. Then, the number of possible values of k is

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