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Let the roots of the polynomial $x^2 + 7x - 2$ be $\alpha$ and $\beta.$ Evaluate $\alpha^2 \beta^2.$

 Aug 4, 2023
 #1
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\(\alpha^2 \beta^2\)

 

1x^2 + 7x - 2

 

By Viete :

 

In a polynomial of the form ax^2 + bx + c, the product of the roots =   c / a

 

Product of the roots =  alpha * beta  =  c/a  =   -2/1 = -2       square both sides

 

(alpha * beta)^2  = (-2)^2

 

alpha^2* beta^2  = 4

 

cool cool cool

 Aug 4, 2023
edited by CPhill  Aug 5, 2023

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