Advertisements
Advertisements
प्रश्न
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
विकल्प
`- c/a`
`c/a`
0
`- b/a`
Advertisements
उत्तर
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is `underlinebb(c/a)`.
Explanation:
According to the question,
We have the polynomial,
ax3 + bx2 + cx + d
We know that,
Sum of product of roots of a cubic equation is given by `c/a`
It is given that one root = 0
Now, let the other roots be α, β
So, we get,
αβ + β(0) + (0)α = `c/a`
αβ = `c/a`
Hence the product of other two roots is `c/a`
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
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 `a(α^2/β + β^2/α) + b(α/β + β/α)`.
If the zeros of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 – 3abc + a2d = 0.
Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4` Verify the relation between the coefficients and the zeroes of the polynomial.
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 α, β are the zeroes of the polynomial f(x) = 5x2 – 7x + 1 then `1/α + 1/β = ?`
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
4x2 – 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:
`4x^2 + 5sqrt(2)x - 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.
`-2sqrt(3), -9`
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 and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
Find a quadratic polynomial whose zeroes are 6 and – 3.
