English Medium कक्षा १० - CBSE Question Bank Solutions

If the equation 9x² + 6kx + 4 = 0 has equal roots, then the roots are both equal to

If ax² + bx + c = 0 has equal roots, then c =

If the equation ax² + 2x + a = 0 has two distinct roots, if 

The positive value of k for which the equation x² + kx + 64 = 0 and x² − 8x + k = 0 will both have real roots, is

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q =

If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then

If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then

If the equation x² − bx + 1 = 0 does not possess real roots, then

If x = 1 is a common roots of the equations ax² + ax + 3 = 0 and x² + x + b = 0,  then ab =

If p and q are the roots of the equation x² – px + q = 0, then ______.

If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax² +bx + 1 = 0 having real roots is

The number of quadratic equations having real roots and which do not change by squaring their roots is

If \[\left( a^2 + b^2 \right) x^2 + 2\left( ab + bd \right)x + c^2 + d^2 = 0\] has no real roots, then

If the sum of the roots of the equation x² − x = λ(2x − 1) is zero, then λ =

If x = 1 is a common root of ax² + ax + 2 = 0 and x² + x + b = 0, then, ab =

The value of c for which the equation ax² + 2bx + c = 0 has equal roots is

If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =

If the sum and product of the roots of the equation kx² + 6x + 4k = 0 are real, then k =

If sin α and cos α are the roots of the equations ax² + bx + c = 0, then b² =

If 2 is a root of the equation x² + ax + 12 = 0 and the quadratic equation x² + ax + q = 0 has equal roots, then q =