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I`d w is the imaginary cube root of unity.then the equation whose roots are 2w+3w^2,2w^2+3w is 1) x^2+5x+7=02) x^2+5x-7=03)x^2-5x+7=04)x^2-5x-7=0

I`d w is the imaginary cube root of unity.then the equation whose roots are 2w+3w^2,2w^2+3w is 1) x^2+5x+7=02) x^2+5x-7=03)x^2-5x+7=04)x^2-5x-7=0

Grade:12

1 Answers

Arun
25763 Points
3 years ago
sum of roots = 2w + 3w^2 + 2w^2 + 3w = 5 w + 5 w^2 = 5(w + w^2) = –5
product of roots = (2w + 3w^2) *(2w^2 + 3w) = 4 w^3 + 9 w^3 + 6(w + w^2) = 4 + 9 – 6 = 7
 
hence quadratic equation will be = 
x^2 –( –5)x + 7 = 0
x^2 + 5 x + 7 = 0

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