Question

if alfa and beta are zeroes of quadratic ploynomial f(x)=x2-px+q then find the values of alpha2+beta2

Answer 1

Hey there
it is given that alfa and beta are the two zero of the polynomial f(x) = x^2 -PX +q .


$\alpha + \beta = - ( \frac{ - p}{1} ) = p \\ and \\ \alpha \beta = > \frac{q}{1} = > \\ \\ = > { \alpha }^{2} + { \beta }^{2} \\ = > ( { \alpha }^{2} + { \beta }^{2} ) - 2 \alpha \beta \\ = > {p}^{2} - 2q$
hope this helps u !!
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Answer 2

f(x)=x2-px+q
standard form of quadratic eq.=ax2+bx+c
if we compare it by f(x) then we get,
a=1, b=(-p), c=q

we know 
if alpha and beta are the zeroes of any quadratic eq. then,