Advertisements
Advertisements
Question
If ๐ผ and ๐ฝ are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of `alpha^4beta^3+alpha^3beta^4`
Solution
Since ๐ผ ๐๐๐ ๐ฝ are the zeroes of the polynomial f(t) = t2 − 4t + 3
Since α + β = 4
Product of zeroes αβ = 3
๐ป๐๐๐๐ α4β3 + α3β4 = α3β3(α + β) = [3]3[4] = 108
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
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`p(x) = x^2 + 2sqrt2x + 6`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
If the zeros of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A.P., prove that 2b3 − 3abc + a2d = 0.
Find the zeroes of the quadratic polynomial `(3x^2 ห x ห 4)` and verify the relation between the zeroes and the coefficients.
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
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 ______.
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
