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Let a and b be the roots of the quadratic x^2 - 5x + 3 = -2x^2 + 11x - 14.  Find the quadratic whose roots are a^2 and b^2.

 

x^2 + ___x + ___

 Mar 27, 2024
 #1
avatar+128794 
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3x^2 - 16x + 17  =  0

 

Product of the roots =   17/3  = ab

(ab)^2 = a^2*b^2  = 289 /  9

2ab =  34/3

 

 

Sum of the roots = 16/3  = a + b         square both sides

 

a^2 + 2ab + b^2  = 256 / 9

 

a^2 + (34/3) + b^2  =  256 /  9

 

a^2 + b^2  =  256 / 9  - 34 /3  =  154 / 9

 

Quadratic  is

 

x^2  - (154/9)x + 289 / 9

 

cool cool cool

 Mar 27, 2024

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