Question

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

Answer 1

Answer:

answer is 9

Step-by-step explanation:

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

divided by alphabeta

Answer 2

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.