English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

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 =

If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =

If a and b are roots of the equation x² + ax + b = 0, then a + b =

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.

If one of the equation ax² + bx + c = 0 is three times times the other, then b² : ac =

If one root the equation 2x² + kx + 4 = 0 is 2, then the other root is

If one of the equation x² + ax + 3 = 0 is 1, then its other root is

If one root of the equation 4x² − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =

If y = 1 is a common root of the equations \[a y^2 + ay + 3 = 0 \text { and } y^2 + y + b = 0\], then ab equals