Advertisements
Advertisements
प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.
`sqrt2 , 1/3`
Advertisements
उत्तर
Given: α + β = `sqrt2`, αβ = `1/3`
Since ax2 + bx + c = kx2 - k(α + β)x + kαβ
or ax2 + bx + c = k[x2 - (α + β)x + αβ]
Or `(ax^2 + bx + c)/k = (x^2 - sqrt2x + 1/3)`
Or `(ax^2 + bx + c)/k = (3x^2 - 3sqrt2x + 1)/3`
Here k is a constant term, by comparing k = 3
Hence, ax2 + bx + c = `3x^2 - 3sqrt2x + 1`
The quadratic polynomial is `3x^2 - 3sqrt2x + 1`.
APPEARS IN
संबंधित प्रश्न
if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify the relation between zeros and its cofficients
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
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) = 6x2 + x – 2, find the value of `alpha/beta + beta/alpha`.
If one zero of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the other, find the value of k.
If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α − β)2.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
Find a cubic polynomial whose zeroes are 2, –3 and 4.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`y^2 + 3/2 sqrt(5)y - 5`
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
If a quadratic equation \[ ax^{2} + bx + c = 0 \] has roots \[ \alpha = 2 \] and \[ \beta = 3 \], which equation has exactly these roots?
