[" Ind "p" are the atros of the quaticatio potynomial "f(x)=x^(2)-m+q" ,prove that "],[qquad beta^(2)quad y^(4)quad 4p^(2)]

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^(2)-px+q, prove that (a^(2))/(beta^(2))+(beta^(2))/(a^(2))=(p^(4))/(q^(2))-(4p^(2))/(q)+2

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^(2)-px+q ,prove that (alpha^(2))/(beta^(2))+(beta^(2))/(alpha^(2))=(p^(4))/(q^(2))-4(p^(2))/(q)+2

If alphaa n dbeta are the zeros of the quadratic polynomial f(x)=x^2-p x+q , prove that (alpha^2)/(beta^2)+(beta^2)/(alpha^2)=(p^4)/(q^2)-(4p^2)/q+2

If alpha and beta are zeros of the quadratic polynomial f(x) = x^(2) - px + q , prove that (alpha^(2))/(beta^(2)) +(beta^(2))/(alpha^(2)) = (p^(4))/(q^(2)) - (4p^(2))/(q) + 2 .

If alpha,beta are the roots of the equation x^2-p x+q=0, prove that (log)_e(1+p x+q x^2)=(alpha+beta)x-(alpha^2+beta^2)/2x^2+(alpha^3+beta^3)/3x^3+

Consider the quadratic polynomial 'f(x)=x^(2)-px+q' where 'f(x)=0' has prime roots alpha and beta and 'p=alpha+beta' , 'q=alpha beta' .If 'p+q=11' and 'a=p^(2)+q^(2)' then find the value of 'f(a)/100' where a is an odd positive integer.

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

IF alphapmsqrtbeta be the roots of the equation x^2+px+q=0 , prove that 1/alphapm1/sqrtbeta will be the roots of the equation (p^2-4q)(p^2x^2+4px)-16q=0 .