Advertisements
Advertisements
प्रश्न
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
Advertisements
उत्तर
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
α4 + β4 = (α2 + β2)2 -2α2 + β2
= ((α + β)2 - 2αβ)2 - 2(αβ)2
`=[(-b/a)^2-2c/a]^2-[2(c/a)^2]`
`=[(b^2-2ac)/a^2]^2-(2c^2)/a^2`
`=((b^2"2ac")^2-2a^2c^2)/a^4`
APPEARS IN
संबंधित प्रश्न
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
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 two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
If α and β are the zeros of the quadratic polynomial f(t) = t2 − 4t + 3, find the value of α4β3 + α3β4.
If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros.
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 zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial whose zeroes are `2/3` and `-1/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial.
Find a cubic polynomial whose zeroes are 2, -3and 4.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.
The zeroes of the quadratic polynomial `4sqrt3"x"^2 + 5"x" - 2sqrt3` are:
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
If all three zeroes of a cubic polynomial x3 + ax2 – bx + c are positive, then at least one of a, b and c is non-negative.
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.
`(-8)/3, 4/3`
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
