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

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