Math, asked by ashsish, 1 year ago

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


kunalpal5218: Is this question complete
kunalpal5218: Please check it again
ashsish: yes
rocka: It's discriminant is weird, you won't get a clean answer

Answers

Answered by rocka
12
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.

Answered by Arshad2003
9

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

( 15 is the final answer ) .

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