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Find the sum of the fourth powers of the roots of x^2 - 3x + 7 = 0.

 Apr 30, 2020
 #1
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Let  the  roots be  a , b

 

By Vieta....the  sum of the roots   - (-3) / 1  =  3

And the product of the roots  = 7/1  =  7

 

So

 

a + b  =   3        square both sides   ⇒  a^2 + 2ab + b^2  =  9      (1)

And

ab  = 7      (2)

 

sub (2)  into 1

 

a^2 + 2 (7) + b^2  = 9

 

a^2  + b^2 + 14  = 9

 

a^2 + b^2  =  -5          square  both sides again

 

a^4  + 2a^2b^2   + b^4  =  25

 

a^4 + b^4  + 2(ab)^2  =   25

 

a^4  + b^4 + 2(7)^2  = 25

 

a^4 + b^4  + 98  =  25

 

a^4 + b^4  =  -73

 

 

cool cool cool

 Apr 30, 2020

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