Advertisements
Advertisements
प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
उत्तर
Given: α + β = 0, αβ = `sqrt5`
Since ax2 + bx + c = k[x2 - (α + β)x + αβ]
Or `(ax^2 + bx + c)/k = (x^2 - 0x + sqrt5)`
or `(ax^2 + bx + c)/k = (x^2 + sqrt5)/1`
Here k is a constant term, by comparing k = 1
Hence, ax2 + bx + c = `x^2 + sqrt5`
The quadratic polynomial is `x^2 + sqrt5`.
APPEARS IN
संबंधित प्रश्न
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
x2 – 2x – 8
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b
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`
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 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 `alpha^4beta^3+alpha^3beta^4`
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
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.
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
If 𝛼, 𝛽 are the zeroes of the polynomial `f(x) = 5x^2 -7x + 1` then `1/∝+1/β=?`
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2x^2 + (7/2)x + 3/4`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`(-8)/3, 4/3`
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`(-3)/(2sqrt(5)), -1/2`
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`
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
