Question

if alpha and beta are the zeroes of the quadratic polynomial x2-5 x+4 then find the value of 1) apha2 + beta2 please tell me answer fast​

Answer 1

Given that α and β are the zeroes of the polynomial

x^2-5x+4x2−5x+4

we have to find the value of

\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha \betaα1+β1−2αβ

x^2-5x+4x2−5x+4

By comparing with standard form ax^2+bx+c=0ax2+bx+c=0

⇒ a=1, b=5 and c=4

\text{Sum of zeroes= }\alpha+\beta=\frac{-b}{a}=-\frac{-5}{1}=5Sum of zeroes= α+β=a−b=−1−5=5

\text{Product of zeroes= }\alpha.\beta=\frac{c}{a}=\frac{4}{1}=4Product of zeroes= α.β=ac=14=4

Now,

\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha \betaα1+β1−2αβ

=\frac{\beta+\alpha}{\alpha \beta}-2\alpha \beta=αββ+α−2αβ

=\frac{5}{4}-2(4)=\frac{5}{4}-8=\frac{-27}{4}=45−2(4)=45−8=4−27