Question

if alpha and betta are zeroes of f (x)=x2-p((x)+qfindalpha square +betta square​

Answer 1

Heya

_______________________________

p( x ) is linear function.

Alfa + Beta = p(x) / 1

And

Alfa × Beta = q/1

=>

Alfa² + Beta² = ( Alfa + Beta )² - 2 Alfa × Beta

=>

Alfa² + Beta² = { p(x) }² - 2q

Answer 2

$\alpha^2+\beta^2=p^2-2q$

Step-by-step explanation:

Given : If alpha and beta are zeroes of  $f(x)=x^2-px+q$

To find : $\alpha^2+\beta^2$ ?

Solution :

If alpha and beta are zeroes of  $f(x)=x^2-px+q$

We know that,

$\alpha+\beta=-\frac{b}{a}$

$\alpha\beta=\frac{c}{a}$

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

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

$\alpha+\beta=p$  .....(1)

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

$\alpha\beta=q$  ......(2)

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

Using (1) and (2),

$\alpha^2+\beta^2=(p)^2-2q$

$\alpha^2+\beta^2=p^2-2q$

#Learn more

If alpha and betta are the zeroes of 2x^2-9x+10, form the polynomial whose zeroes are 1/alpha and 1/betta​

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