Advertisements
Advertisements
Question
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
4u2 + 8u
Advertisements
Solution
4u2 + 8u = 4u(u + 2)
= 4[u - 0][u - (-2)]
For p(u) = 0, we have
Either 4u = 0
u = -2
∴ The zeroes of 4u2 + 8u are 0 and -2.
Relationship between the zeroes and the coefficients of the polynomial
Sum of the zeroes = `-("Coefficient of " u)/("Coefficient of " u^2)`
= `0 + (-2) =(-(8))/4`
= -2 = -2
Also product of the zeroes = `"Constant term"/("Coefficient of " u^2)`
= `0 xx (-2) = 0/4`
= 0 = 0
Thus, the relationship between the zeroes and the coefficients in the polynomial 4u2 + 8u is verified.
APPEARS IN
RELATED QUESTIONS
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
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(2beta)/alpha`
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
If 𝛼, 𝛽 are the zeroes of the polynomial f(x) = x2 + x – 2, then `(∝/β-∝/β)`
Define a polynomial with real coefficients.
If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]
If two zeroes of the polynomial x3 + x2 − 9x − 9 are 3 and −3, then its third zero is
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
A quadratic polynomial, whose zeroes are –3 and 4, is ______.
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
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:
5t2 + 12t + 7
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
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.
`21/8, 5/16`
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
