The real number $k$ for which the equation $2x^2 + 3x + k = 0$ has two distinct real roots in the interval $[0, 1]$.

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ such that $\min f(x) > \max g(x)$,then the relation between $b$ and $c$ is

For what minimum value of $k$ do both roots of the equation $x^2 - 8kx + 16(k^2 - k + 1) = 0$ exist,are real,distinct,and at least $4$?

If non-zero real numbers $b$ and $c$ are such that $\min \,f(x) > \max \,g(x)$,where $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$ for $x \in R$; then $\left| \frac{c}{b} \right|$ lies in the interval

If $f(x) = x^2 - 2(4K - 1)x + g(K) > 0$ for all $x \in R$ and for $K \in (a, b)$. If $g(K) = 15K^2 - 2K - 7$,then:

If the roots of ${x^2} + x + a = 0$ exceed $a$,then