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Let a and b be the roots of the quadratic x^2 - 5x + 3 = 2x^2 - 7x + 11.  Find the quadratic whose roots are a^4 and b^4.

 Jul 28, 2022
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Rearrange the given equation as

 

x^2 - 2x +  8  =  0

 

(x - 4) ( x + 2)  = 0

 

The roots  are   4 , -2 =   a , b

 

4^4 =  256 =  a^4

(-2)^4  = 16 = b^4

 

The sum of these roots =  -b  in the new quadratic  = -272

The product of these roots = c in the new quadratic =   4096

 

The new quadratic =  x^2 - 272x + 4096

 

 

cool cool cool

 Jul 28, 2022

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