The positive root of $x^{2}-78.8=0$ after the first approximation by the Newton-Raphson method,assuming the initial approximation to the root is $14$,is:

If ${x^2} + {y^2} = 25$ and ${xy} = 12$,then the possible values of $x$ are:

What is the product of the real roots of the equation ${t^2}{x^2} + |x| + 9 = 0$?

If the roots of the equation $x^2 - 2cx + ab = 0$ are real and unequal,then the roots of the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$ are

The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ such that $a \neq b \neq c$ from the set $\{0, 1, 2, 4\}$ is:

The equation $e^{4x} + 8e^{3x} + 13e^{2x} - 8e^x + 1 = 0, x \in R$ has: