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Quadratics with new roots. Create new quadratic from given roots (Alpha and Beta)

Hello guys, could I get some help with this question? Please :smile:

:smile:

:
Create new quadratic equation with new roots of 1/ALPHA^2 and 1/BETA^2 (1/ means 1 over as in a fraction)
From given equation: 5x^2 -2x +4 =0.
I think I have to first find the sum and product of actual roots then use the values for the new roots sum and product.
I did that and I am still getting the wrong answer, in the back of the book the correct answer is 16x^2 + 36x +25 =0 (way different than what I get)

(edited 7 years ago)

You have the sum of the new roots as

\displaystyle \frac{1}{\alpha ^2} + \frac{1}{\beta ^2}

.
Add these two fractions as you normally would add any fractions and give it in terms of

(\alpha +\beta )

and

\alpha \beta

as you already know the values of.

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