The integer ' `k` ',for which the inequality `x^(2)-2(3k-1)x+8k^2-7>0` is valid for every `x in R` is

25. The integer k for which the inequality x 2 -2(4k-1)x +15k 2 - 2k-7 > 0 is valid for any real x is (a) 2 (b) 3 (c) 4 (d) infinite

The number of integral values of k for which the inequality x^(2)-2(4k-1)x+15k^(2)-2k-7 ge0 hold for x in R are _____________

If k_(1) and k_(2) ( k_(1) gt k_(2) ) are two non-zero integral values of k for which the cubic equation x^(3)+3x^(2)+k=0 has all integer roots, then the value of k_(1)-k_(2) is equal to_______

The value of k for which the sum of the squares of the roots of 2x^(2)-2(k-2)x-k=0 is least is

The set of value of k (k in R) for which the equation x ^(2) -4 |x|+3 -|k-1|=0 will have exactly four real roots, is:

The set of vlaue of k (k in R) for which the equation x ^(2) -4 |x|+3 -|k-1|=0 will have exactly four real roots, is:

The positive value of k for which the equation x^2+k x+64=0 and x^2-8x+k=0 will both have real roots, is (a)4 (b) 8 (c) 12 (d) 16

The positive value of k for which the equation x^2+k x+64=0 and x^2-8x+k=0 will both have real roots, is (a) 4 (b) 8 (c) 12 (d) 16

The value of k for which the equation 3x^(2) + 2x (k^(2) + 1) + k^(2) - 3k + 2 = 0 has roots of opposite signs, lies in the interval

Find the least integral value of 'k' for which the quadratic polynomial (k-1)x^(2) + 8x + k + 5 gt 0 AA x in R