Advertisements
Advertisements
प्रश्न
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
विकल्प
x2 + 3x + 2
x2 – 3x + 2
x2 – 3x – 2
x2 + 3x – 2
Advertisements
उत्तर
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is x2 + 3x + 2.
Explanation:
Given that,
Sum of zeroes = – 3
Product of zeroes = 2
Quadratic Polynomial is given by:
x2 – (Sum of zeroes)x + (Product of zeroes)
So, P(x): x2 – (– 3) x + 2
Required Quadratic Polynomial is x2 + 3x + 2.
APPEARS IN
संबंधित प्रश्न
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
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(y) = 5y2 – 7y + 1, find the value of `1/α + 1/β`.
If α and β are the zeros of the quadratic polynomial f(x) = x2 – px + q, prove that `alpha^2/beta^2 + beta^2/alpha^2 = p^4/q^2 - (4p^2)/q + 2`.
Verify that 5, –2 and `1/3` are the zeroes of the cubic polynomial p(x) = (3x3 – 10x2 – 27x + 10) and verify the relation between its zeros and coefficients.
If 3 and –3 are two zeroes of the polynomial (x4 + x3 – 11x2 – 9x + 18), find all the zeroes of the given polynomial.
If α, β are the zeroes of the polynomial f(x) = 5x2 – 7x + 1 then `1/α + 1/β = ?`
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 α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
For the cubic equation \[ ax^{3} + bx^{2} + cx + d = 0 \] with roots \[ \alpha, \beta, \gamma \], the pairwise product \( \alpha\beta + \beta\gamma + \gamma\alpha \) equals:
