Question

if alpha and beta are the zeros of polynomial PX equal to 5 x square + 5 x + 1 then find the value of Alpha square plus beta square and Alpha to the power minus 100 to the power 1 minus 1

Answer 1

Solution:

For, a polynomial ,$ax^2+b x+c=0$, having roots , m and n

Sum of roots

$= m + n=\frac{-b}{a}\\\\ {\text{product of roots}}=m n=\frac{c}{a}$

It is given that, α and β are the zeros of polynomial P(x).

$P(x)=5 x^2+5 x+1$

α+β

$=\frac{-5}{5}=-1$

α  β

$=\frac{1}{5}$

1. α²+β²

  =(α+β)²-2αβ

  $=(-1)^2-2\times \frac{1}{5}\\\\=1-\frac{2}{5}\\\\=\frac{3}{5}$

$2.[(\alpha)^{-100}]^{1-1} =[(\alpha)^{-100}]^{0}=(\alpha)^0=1$