Advertisements
Advertisements
प्रश्न
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
Advertisements
उत्तर
Given: α + β = `-1/4`, αβ = `1/4`
Since ax2 + bx + c = k[x2 - (α + β)x + αβ]
Or `(ax^2 + bx + c)/k = x^2 - (-1/4x) + 1/4)`
Or `(ax^2 + bx + c)/k = (4x^2 + 4x + 1)/4`
Here k is a constant term, by comparing k = 4
Hence, ax2 + bx + c = `4x^2 + 4x + 1`
The quadratic polynomial is `4x^2 + 4x + 1`.
APPEARS IN
संबंधित प्रश्न
Prove relation between the zeros and the coefficient of the quadratic polynomial ax2 + bx + c
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
`p(x) = x^2 + 2sqrt2x + 6`
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) = x2 − px + q, prove that `alpha^2/beta^2+beta^2/alpha^2=p^4/q^2-(4p^2)/q+2`
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, -2 and -24 respectively.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
5t2 + 12t + 7
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`
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
