List of top Mathematics Questions on Quadratic Equations asked in Bihar Board X

If one zero of the polynomial \( (a^2 + 9)x^2 + 13x + 6a \) is reciprocal of the other, find \( a \).

Find the discriminant of the quadratic equation \( \sqrt{2}x^2 - x - \sqrt{2} = 0 \) and hence find the nature of the roots.

For what value of \( k \) will the equation \( kx(x-2) + 6 = 0 \) have equal roots?

For what value of \( k \) equations \( kx + y = 1 \) and \( (k-1)x + 2y = 3 \) have no solution?

Write the solution of the equation \( 3x + y = 11 \) in natural numbers.

Find the roots of the equation \( \frac{1}{x} - \frac{1}{x-2} = 3 \), \( x \neq 0,2 \).

If the product of the roots of the quadratic equation \( x^2 - 5x + p = 10 \) is -4, then the value of \( p \) is:

What is the nature of the roots of the quadratic equation \( \frac{4}{3}x^2 - 2x + \frac{3}{4} = 0 \)?

If one root of the quadratic equation \( y^2 + 3y - 18 = 0 \) is -6, then its other root is:

If \( x = 2 \) is a common root of the equations \( 2x^2 + 2x + p = 0 \) and \( qx + qx + 18 = 0 \), then the value of \( (q - p) \) is:

Which of the following is a quadratic equation?

Find the discriminant of the quadratic equation \( 9x^2 - 6x + 1 = 0 \) and hence find the nature of the roots.

For what values of \( k \) does the quadratic equation \( (k+1)x^2 - 2(k-1)x + 1 = 0 \) have equal roots?

For what value of \( k \), do the equations \( kx + y = 1 \) and \( (k+1)x + 2y = 3 \) have no solution?

Find the roots of the equation \( x + \frac{1}{x} = 3, \quad x \neq 0 \).

Which of the following polynomial has roots 4 and -2?

If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( p(x) = x^2 + 3x - 4 \), then the value of \( \frac{\alpha \beta}{4} \) is:

If one zero of the polynomial \( q(x) \) is -3, then one factor of \( q(x) \) is: