Advertisements
Advertisements
Question
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Let α, β and γ be the zeroes of a cubic polynomial and given that two of the given zeroes have value 0.
Let β = γ = 0 and
p(x) = (x – α)(x – β)(x – γ)
= (x – α)(x – 0)(x – 0)
= x3 – αx2
Which does not have linear and constant terms.
APPEARS IN
RELATED QUESTIONS
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
4s2 – 4s + 1
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
t2 – 15
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
`q(x) = sqrt(3)x^2 + 10x + 7sqrt(3)`
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 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(x) = x2 − 3x − 2, find a quadratic polynomial whose zeroes are `1/(2alpha+beta)+1/(2beta+alpha)`
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are α + 2, β + 2.
Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
By actual division, show that x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.
On dividing 3x3 + x2 + 2x + 5 is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If two zeros x3 + x2 − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is
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
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 factorization.
`21/8, 5/16`
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`v^2 + 4sqrt(3)v - 15`
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
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.
For the quadratic equation \[ ax^{2} + bx + c = 0 \] with roots \[ \alpha, \beta \], which expression gives the product of the roots \( \alpha\beta \)?
