Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If a and are the zeros of the quadratic polynomial f(x) = ЁЭСе2 − ЁЭСе − 4, find the value of `1/alpha+1/beta-alphabeta`
Advertisements
рдЙрддреНрддрд░
Since ЁЭЫ╝ + ЁЭЫ╜ are the zeroes of the polynomial: ЁЭСе2 − ЁЭСе − 4
Sum of the roots (α + β) = 1
Product of the roots (αβ) = −4
`1/alpha+1/beta-alphabeta`
`=(alpha+beta)/(alphabeta)-alphabeta`
`=(1/-4)+4=(-1/4)+4=(-1+16)/4=15/4`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
If ЁЭЫ╝ and ЁЭЫ╜ are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
If a and 3 are the zeros of the quadratic polynomial f(x) = x2 + x − 2, find the value of `1/alpha-1/beta`.
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
Find the zeroes of the quadratic polynomial `(3x^2 ╦Ч x ╦Ч 4)` and verify the relation between the zeroes and the coefficients.
Find the quadratic polynomial, sum of whose zeroes is `sqrt2` and their product is `(1/3)`.
If f(x) =` x^4 – 3x^2 + 4x + 5` is divided by g(x)= `x^2 – x + 1`
If f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
Define a polynomial with real coefficients.
If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =
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
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial 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 factorisation.
`-2sqrt(3), -9`
Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`y^2 + 3/2 sqrt(5)y - 5`
