Question

if alpha and beta are the zeroes of polynomials 25x2+ 25x+5 then find 1/alpha2+1/beta2

Answer 1

Let the zeroes be $\alpha \ and \ \beta$

We need to find $\frac{1}{ \alpha ^{2}} + \frac{1}{ \beta^{2}}$

Factorising the polynomial we have:

$25x^{2}+ 25x+ 5 = 5 (5 x^2 + 5 x + 1)$

Solving using quadratic equation $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ we have:

[tex]x_{1,\:2}=\frac{-5\pm \sqrt{5^2-4\cdot \:5\cdot \:1}}{2\cdot \:5} \\ \\ \\ x = \frac{-5+\sqrt{5}}{10} \\ x = \frac{-5-\sqrt{5}}{10}[/tex]

Now you just need to put in the values of alpha and beta as x1 and x2. I feel it's tedious to do the calculation so I'll just leave it here.

Answer 2

Hi.... plz find the answer in the following attachment below.

( 15 is the final answer ) .