If $f(x) = ax^{2} + bx + 2$ and $f(1) = 4, f(3) = 38$,then $a - b = $

If the resultant of two forces of magnitudes $P$ and $Q$ acting at a point at an angle of $60^\circ$ is $\sqrt{7}Q$,then $P/Q$ is

Let $f(x) = ax^{2} + bx + c$ be such that $f(1) = 3$,$f(-2) = \lambda$,and $f(3) = 4$. If $f(0) + f(1) + f(-2) + f(3) = 14$,then $\lambda$ is equal to...

If $a, b, c \in Q$,then the roots of the equation $(b + c - 2a)x^2 + (c + a - 2b)x + (a + b - 2c) = 0$ are

Let $a \ne a_1 \ne 0,$ $f(x) = ax^2 + bx + c,$ $g(x) = a_1x^2 + b_1x + c_1,$ and $p(x) = f(x) - g(x).$ If $p(x) = 0$ only for $x = -1$ and $p(-2) = 2,$ then the value of $p(2)$ is

If $b_{1} b_{2} = 2(c_{1} + c_{2})$ and $b_{1}, b_{2}, c_{1}, c_{2}$ are all real numbers, then at least one of the equations $x^{2} + b_{1} x + c_{1} = 0$ and $x^{2} + b_{2} x + c_{2} = 0$ has