Quadratic Equations (10)

Solve for x:

$$ \frac{1}{x+1} +\frac{3}{5x+1} = \frac{5}{x+4}, x\ne-1, -\frac{1}{5}, -4 $$

Find the roots of the quadratic equation $ x^2 - x - 2 = 0 $

Find the discriminant of the quadratic equation $ 3x^2 - 2x + \frac{1}{3} = 0 $ and  hence find the nature of its roots

Assertion (A): If one root of the quadratic equation $ 4x^2 − 10x + (k − 4) = 0 $ is reciprocal of the other, then value of k is

Which of the following is not a quadratic equation?

1. $ 2(x −1)^2 = 4x^2 − 2x + 1

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is

A quadratic polynomial the sum and product of whose zeroes are -3 and 2 respectively, is

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more

A motor boat whose speed is 18 km/hr in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot. Find the

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by

If x = 3 is one root of the quadratic equation x² - 2kx - 6 = 0, then find the value of k.

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.

Two taps running together can fill a tank in 3$\frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank, then how much

If ad $\ne$ bc, then prove that the equation

(a² + b²)x² + 2(ac + bd)x + (c² + d²)

Find the value of p, for which one root of the quadratic equation $px^2 - 14x + 8 = 0$ is 6 times the other.

In a class test, the sum of Arun’s marks in Hindi and English is 30. Had he got 2 marks more in Hindi and 3 marks less in English, the product of

Write all the values of p for which the quadratic equation x² + px + 16 = 0 has equal roots. Find the roots of the equation so

Find the nature of roots of the quadratic equation $2x^2 - 4x + 3 = 0$