For the quadratic equation \(x^{2} + 4x + b = 0\) , the discriminant D = ................... .

If \(\sqrt {x+ \sqrt {x +\sqrt {x +.... \infty }}} = 6\) . then find the value of x.

If p and q are the roots of quadratic equation \(x^{2} - px + q = 0\) , then find the values of p and q.

If 1 is a root of the equations \(ay^{2}+ ay + 3 = 0\) and \(y^{2}+y + b = 0\) , then find ab.      

If the discriminant of a quadratic equation is zero, then the equation has no real roots.

A quadratic equation in the variable x is of the form \(ax^{2} + bx + c =0, a \neq 0\), where a, b and c are real numbers.

Any equation of the form p(x) = 0, where p(x) is a polynomial of degree one, is a quadratic equation.

Check whether the following are quadratic equations: (2x – 1)(x – 3) = (x + 5)(x – 1)

Check whether the following are quadratic equations: x² + 3x + 1 = (x - 2)²

Check whether the following are quadratic equations: (x+2)³=2x(x²-1)

Solve for x: \(x^2+5x-(a^2+a-6)=0\)

A two digit number is such that the product of its digits is 15. If 18 is added to the number, the digits interchange their places. Find the number.

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B to finish the work.

Find three consecutive positive integers whose product is equal to sixteen times their sum.