English Medium कक्षा १० - CBSE Question Bank Solutions

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 zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

g(x) = a(x² + 1) – x(a² + 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 α²β + αβ².

If a and 3 are the zeros of the quadratic polynomial f(x) = x² + x − 2, find the value of `1/alpha-1/beta`.

If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x² − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`

If α and β are the zeros of the quadratic polynomial f(t) = t² − 4t + 3, find the value of α⁴β³ + α³β⁴.

If α and β are the zeros of the quadratic polynomial p(y) = 5y² – 7y + 1, find the value of `1/α + 1/β`.

If α and β are the zeros of the quadratic polynomial p(s) = 3s² − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`

If α and β are the zeros of the quadratic polynomial f(x) = x² – px + q, prove that `alpha^2/beta^2 + beta^2/alpha^2 = p^4/q^2 - (4p^2)/q + 2`.

If the squared difference of the zeros of the quadratic polynomial f(x) = x² + px + 45 is equal to 144, find the value of p.