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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 + ___

 May 22, 2024
 #1
avatar+129512 
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Rearrange as

3x^2 - 16x + 17  = 0

 

ab = 17/3   →  2ab  = 34/3     

 

 a + b = 16/3      square both sides

 a^2 + 2ab + b^2 = 256/9

 a^2  + 34/3 + b^2  = 256/9

 a^2 + b^2  = 154/9

 

ab = 17/3

(ab)^2 = 289/9

a^2 * b^2  = 289 / 9

 

The polynomial is

 

x^2  - (154/9)x + 289 / 9

 

 

cool cool cool

 May 23, 2024

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