# maths

If alpha and beta are the zeros of the polynomial p(x)=x^2+x+1 then find the value of 1÷alpha+1÷beta 2)alpha^2+beta^2

1. 👍 0
2. 👎 0
3. 👁 55
1. I will use a for alpha and b for beta

then from the properties of zeros of a quadratic
a+b = -1
ab = 1

then 1/a + 1/b
= (b+a)/(ab) = -1/1 = -1

a^2 + b^2
= (a+b)^2 - 2ab
= (-1)^2 - 2(1)
= 1 - 2 = -1

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### Math ( Polynomial )

This time three questions - 1. If (x^2 - 1 ) is a factor of polynomial ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0. 2. Let R1 and R2 be the remainders when polynomials x^3 + 2x^2 - 5ax - 7 and x^ 3 + ax^2 - 12 x +

asked by Jack on April 13, 2013
2. ### Math ( Polynomial )

This time three questions - 1. If (x^2 - 1 ) is a factor of polynomial ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0. 2. Let R1 and R2 be the remainders when polynomials x^3 + 2x^2 - 5ax - 7 and x^ 3 + ax^2 - 12 x +

asked by Jack on April 13, 2013
3. ### maths

if alpha and beta are the zeros of the polynomial 2x^2-4x+5 then find the values of (i)alpha^2+beta^2 (ii)1/alpha^2+1/beta^2 (iii)(r)alpha/beta+(r)beta/alpha (iv)alpha^-1+beta^-1

asked by echo on June 7, 2012
4. ### Math

If alpha and beta are the zeros of the polynomial ax^2 + bx + c then evaluateA. (alpha)^2 / beta + (beta)^2 / alpha B. alpha^2 .beta + alpha.beta^2 C. 1/(alpha)^4 + 1/(beta)^4. Please work the complete solution.

asked by Steve on April 14, 2013
5. ### Maths

If alpha and beta are the zeros of the polynomial 4x square-16x+15, form a polynomial whose zeros are alpha by beta,beta by alpha

asked by Kanisri on August 11, 2016
6. ### sharma

if alpha and beta are the zero's of quadratic polynomial f(x) =x*x-x-2 find a polynomial who's zeros are 2 alpha +1 and 2 bita + 1 ?

asked by Ganesh on December 31, 2017
7. ### maths

if alpha and beta are the zeros of p(x)=3x^2-7x-6.find a polynomial whose zeros are alpha^2 and beta^2

asked by Niharika on June 27, 2016
8. ### Math

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta = 0. Prove that : c^2 + ac + b + 1 = 0. Please work the complete solution.

asked by Watson on April 23, 2013
9. ### Math

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta -1 = 0. Prove that : c^2 + ac + b + 1 = 0. Please work the complete solution

asked by Steve on April 27, 2013
10. ### Math

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta = 0. Prove that : c^2 + ac + b + 1 = 0. Please work the complete solution.

asked by Watson on April 23, 2013

More Similar Questions