Math, asked by bhumikaasri, 10 months ago

If alpha and beta are the zeroes if the polynomial x^2 — 6x +8, then the value of alpha^2/beta + beta^2/ alpha

Answers

Answered by v2956823
9

Answer:

answer is 9

Step-by-step explanation:

alpha cube + beta cube + 3alphabeta(alpha+beta)

divided by alphabeta

Answered by qwmagpies
5

Given: Alpha and beta are the zeroes of the polynomial

x^2 — 6x +8

To find: We have to find

 { \alpha }^{2}  +  { \beta }^{2}

Solution:

The equation is-

x^2 — 6x +8

The roots of the equation are as follows-

x^2 — 6x +8 \\  {x}^{2}  - 4x - 2x + 8 = 0 \\ x(x - 4) - 2(x - 4) = 0 \\ (x - 4)(x - 2) = 0 \\ x = 4 \\ x = 2

The values of alpha and beta are respectively 4 and 2.

Thus, the value of the sum of the square of alpha and the square of beta is as follows-

 { \alpha }^{2}  +  { \beta }^{2}  \\  {4}^{2}  +  {2}^{2}  \\  = 16 + 4 \\  = 20

The value is 20.

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