List of top Mathematics Questions on Quadratic Equations asked in KEAM

If \( a \) and \( b \) are the non-zero distinct roots of \( x^2 + ax + b = 0 \), then the minimum value of \( x^2 + ax + b \) is:

Let \( x_1 \) and \( x_2 \) be the roots of the equation \( x^2 + px - 3 = 0 \). If \( x_1^2 + x_2^2 = 10 \), then the value of \( p \) is equal to:

If \( x \) and \( y \) are the roots of the equation \( x^2 + bx + 1 = 0 \), then the value of \( \frac{1}{x+b} + \frac{1}{y+b} \) is:

The equations \( x^5 + ax + 1 = 0 \) and \( x^6 + ax^2 + 1 = 0 \) have a common root. Then \( a \) is equal to:

If the product of roots of the equation \( mx^2 + 6x + (2m - 1) = 0 \) is \( -1 \), then the value of \( m \) is:

Let \( x=2 \) be a root of \( y = 4x^2 - 14x + q = 0 \). Then \( y \) is equal to:

If \( x_1 \) and \( x_2 \) are the roots of \( 3x^2 - 2x - 6 = 0 \), then \( x_1^2 + x_2^2 \) is equal to:

If the roots of the equation \( (x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a) = 0 \) are equal, then \( a^2 + b^2 + c^2 = \)

If one root of a quadratic equation is \( \frac{1}{1+\sqrt{3}} \), then the quadratic equation is

If the difference between the roots of \( x^2 + 2px + q = 0 \) is two times the difference between the roots of \( x^2 + qx + \frac{p}{4} = 0 \), where \( p \neq q \), then

Sum of the roots of the equation \( |x-3|^2 + |x-3| - 2 = 0 \) is equal to

The quadratic equation whose roots are three times the roots of the equation \( 2x^2 + 3x + 5 = 0 \), is

If \(x\) is real number, then \( \frac{x}{x^2 - 5x + 9} \) must lie between

If the roots of the equation \( x^2 + 2bx + c = 0 \) are \( \alpha \) and \( \beta \), then \( b^2 - c = \)

The equation whose roots are the squares of the roots of the equation \( 2x^2 + 3x + 1 = 0 \) is:

If \( z_1 = 2\sqrt{2}(1 + i) \) and \( z_2 = 1 + i\sqrt{3} \), then \( z_1^2 z_2^3 \) is equal to:

If the complex numbers \( z_1, z_2 \) and \( z_3 \) denote the vertices of an isosceles triangle, right angled at \( z_1 \), then \( (z_1 - z_2)^2 + (z_1 - z_3)^2 \) is equal to:

If the roots of \( x^2 - ax + b = 0 \) are two consecutive odd integers, then \( a^2 - 4b \) is:

If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + 3x - 4 = 0 \), then \( \frac{1}{\alpha} + \frac{1}{\beta} \) is equal to:

If the roots of \( x^2 - ax + b = 0 \) are two consecutive odd integers, then \( a^2 - 4b \) is:

If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + 3x - 4 = 0 \), then \( \frac{1}{\alpha} + \frac{1}{\beta} \) is equal to:

If the roots of the equation \( x^2 + 2bx + c = 0 \) are \( \alpha \) and \( \beta \), then \( b^2 - c = \)

The equation whose roots are the squares of the roots of the equation \( 2x^2 + 3x + 1 = 0 \) is:

If \( z_1 = 2\sqrt{2}(1 + i) \) and \( z_2 = 1 + i\sqrt{3} \), then \( z_1^2 z_2^3 \) is equal to:

If the complex numbers \( z_1, z_2 \) and \( z_3 \) denote the vertices of an isosceles triangle, right angled at \( z_1 \), then \( (z_1 - z_2)^2 + (z_1 - z_3)^2 \) is equal to: