Advertisements
Advertisements
प्रश्न
Find a cubic polynomial whose zeroes are `1/2, 1 and -3.`
Advertisements
उत्तर
If the zeroes of the cubic polynomial are a, b and c then the cubic polynomial can be found as
`x^3 – (a + b + c)x^2 + (ab + bc + ca)x – abc` .............(1)
Let a = `1/2, b=14 and c=-3`
Substituting the values in (1), we get
`x^3-(1/2+1-3)x^2+(1/2-3-3/2)x-(-3/2)`
⇒ `x^3-(-3/2)x^2-4x+3/2`
`⇒ 2x^3+3x^2-8x+3`
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 a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case
x3 – 4x2 + 5x – 2; 2, 1, 1
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(s) = 3s2 − 6s + 4, find the value of `alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta`
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `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`
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
