Question

if alpha and beta are zeroes of polynomial x2+x-1, then find the value of alpha square beta +alpha beta square​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The value of the expression is $\alpha ^2\beta +\alpha \beta^2=1$

Step-by-step explanation:

Given : If alpha and beta are zeroes of polynomial $x^2+x-1$.

To find : The value of alpha square beta +alpha beta square​ ?

Solution :

Writing the relationship between the zeros and coefficient.

In polynomial $x^2+x-1$.

Here, a=1, b=1 and c=-1

The sum of zeros is $\alpha+\beta=-\frac{b}{a}$

$\alpha+\beta=-\frac{1}{1}$

$\alpha+\beta=-1$  .....(1)

The product of zeros is $\alpha \beta =\frac{c}{a}$

$\alpha \beta =\frac{-1}{1}$

$\alpha \beta =-1$  .....(2)

Now, expression is $\alpha ^2\beta +\alpha \beta^2$

$\alpha ^2\beta +\alpha \beta^2=\alpha\beta(\alpha+\beta)$

Substitute (1) and (2),

$\alpha ^2\beta +\alpha \beta^2=(-1)(-1)$

$\alpha ^2\beta +\alpha \beta^2=1$

Therefore, the value of the expression is $\alpha ^2\beta +\alpha \beta^2=1$

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