English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

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:\[px(x - 3) + 9 = 0\]

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

\[4 x^2 + px + 3 = 0\]

Find the values of k for which the quadratic equation 

\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.

Find the values of p for which the quadratic equation 

If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.

If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\]  has equal roots, find the value of k.

If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.

Find the value of p for which the quadratic equation 

\[\left( p + 1 \right) x^2 - 6(p + 1)x + 3(p + 9) = 0, p \neq - 1\] has equal roots. Hence, find the roots of the equation.

Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.

If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.