Question

If alpha and beta are the zeroes of polynomial x square +4x-5,find the value of alpha square +beta square.

Answer 1

Step-by-step explanation:

alpha + beta = -4

alpha*beta = -5

Now ,

alpha² + beta²

= (alpha + beta)² - 2alpha*beta

= (-4)² - 2(-5)

= 16 + 10

= 26

Answer 2

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$px = {x}^{2} + 4x - 5$

This is a quadratic equation hence 2 zeroes alpha and beta

Here

A=1

B=4

C=-5

Now

$\alpha + \beta = - b \div a$

Now

Alpha+ beta= - 4/1hence

Alpha+beta= 4/1

Now

$\alpha \beta = c \div a$

Now

Alpha *beta= - 5/1

Now we have to find alpha square + beta square

Now

(alpha square) + (beta square) = (4/1) whole square

Now a^2+b^2 CAN BE WRITTEN AS

(a+b) ^2- 2 ab= 16/1

Now we know alpha + beta and alpha beta

Put the values and solve