English Medium कक्षा १० - CBSE Question Bank Solutions

Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]

Solve the following quadratic equations by factorization:

\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5\]

Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]

Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1}, x \neq - 1, \frac{1}{3}\]

Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]

Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]

Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]

Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].

Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]

Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2};   x \neq 1,  - 2,   2\] 

Solve the following quadratic equations by factorization: \[\frac{1}{2a + b + 2x} = \frac{1}{2a} + \frac{1}{b} + \frac{1}{2x}\]

Solve the following quadratic equations by factorization:

\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]

Solve the following quadratic equations by factorization:

\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]

Find the values of k for which the roots are real and equal in each of the following equation:

\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]

In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]

Find the value of k for which the following equations have real and equal roots:

\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]

Find the value of k for which the following equations have real and equal roots:

\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]

Find the value of k for which the following equations have real and equal roots:

\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]

Find the values of k for which the roots are real and equal in each of the following equation:

\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]

Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]