Advertisements
Advertisements
Question
Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the product of the other two zeroes is ______.
Options
`- c/a`
`c/a`
0
`- b/a`
Advertisements
Solution
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
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
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 α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
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 p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
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 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.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
The zeroes of the polynomial r(t) = -12t2 + (k - 3)t + 48 are negative of each other. Then k is ______.
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
The number of polynomials having zeroes as –2 and 5 is ______.
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`
The only value of k for which the quadratic polynomial kx2 + x + k has equal zeros is `1/2`
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
