Advertisements
Advertisements
Question
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α2β + αβ2
Advertisements
Solution
f(x) = ax2 + bx + c
α + β = `(-b/a)`
αβ = `c/a`
since α + β are the roots (or) zeroes of the given polynomials
then
α2β + αβ2
αβ(α + β)
`=c/a((-b)/a)`
`=(-bc)/a^2`
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
1, 1
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
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 zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`
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`
Find the zeroes of the quadratic polynomial 2x2 – 11x + 15 and verify the relation between the zeroes and the coefficients.
Find the quotient and the remainder when f(x) = x4 – 3x2 + 4x + 5 is divided by g(x) = x2 – x + 1.
If 1 and –2 are two zeroes of the polynomial (x3 – 4x2 – 7x + 10), find its third zero.
If α, β are the zeroes of the polynomial f(x) = x2 + x – 2, then `(α/β - α/β)`.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
What will be the expression of the polynomial?
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes is ______.
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`
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
