English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?

If ad ≠ bc, then prove that the equation (a² + b²) x² + 2 (ac + bd) x + (c² + d²) = 0 has no real roots.

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9^th terms.

Find the sum of first 8 multiples of 3

Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)`  and `(2 - sqrt3)`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

`p(x) = x^2 + 2sqrt2x + 6`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`q(x)=sqrt3x^2+10x+7sqrt3`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`f(x)=x^2-(sqrt3+1)x+sqrt3`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`g(x)=a(x^2+1)-x(a^2+1)`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α²β + αβ²

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α⁴ + β⁴ 

If α and β are the zeroes of the quadratic polynomial f(x) = ax² + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`.

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`

If α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c, then evaluate :

`a(α^2/β+β^2/α)+b(α/β+β/α)`

If α and β are the zeros of the quadratic polynomial f(x) = 6x² + x − 2, find the value of `alpha/beta+beta/alpha`.

If a and are the zeros of the quadratic polynomial f(x) = 𝑥² − 𝑥 − 4, find the value of `1/alpha+1/beta-alphabeta`

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x² − 5x −1, find the value of α^2β + αβ².