Math

posted by Steve

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.

1. Reiny

let the two roots be m and n

then we want
m^2/n + n^2/m
= (m^3 + n^3)/(mn)
= (m+n)(m^2 -mn + n^2)/(mn) , where m^2 + n^2 = (m+n)^2 - 2mn

= (m+n)( (m+n)^2 - 3mn)/(mn)

now from a^2 + bx + c = 0
m+n = -b/a
and mn = c/a

(m+n)( (m+n)^2 - 3mn)/(mn)
= (-b/a)( (-b/a)^2 - 3(c/a) )/(c/a)
which I reduced to
-b^3/(ca^2) - 3

check my algebra and do the others the same way

2. dhami

idk... its wrong.. or not specific.. (abv one)

We know for any quadratic polynomial f(x)=ax^2+bx+c with roots alpha(p) and beta(q)
(x-p)(x-q)= K[x^2-(p+q)x+pq]
So we express (p+q) as -b/a and pq as c/a.....
A.)(p^2/q) + (q^2/p)=?
By simply taking LCM, we can write the above statement as
(p^3+q^3)/pq
=(p+q)(p^2+q^2-pq)[identity used]
{Now what you must understand here is that we can only substitute the values of the sum and products of the roots- so our attempt now must be towards expressing this in the form of (p+q) or pq only}
=(p+q)((p+q)^2-3pq)
On reducing by substitution-
You will obtain (3abc-b^3)/a^3

Similar Questions

1. Math

how i solve this two equations ib order to find alpha and beta 2=cos(alpha)+1.341cos(beta) 2=sin(alpha)-1.341sin(beta)
2. Calculus

The question will first read in English followed by a reading in French. *************************************** If alpha + 2 beta = pi/4 AND tan beta = 1/3. What would tan alpha mesure?
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
4. trig

evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(beta-alpha) …
5. 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 + …
6. 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 + …
7. 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.
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.
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
10. 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

More Similar Questions