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If the roots α and β (α + β ≠ 0) of the quadratic equation ax^2 + bx + c = 0 are real and of opposite sign. Then show that roots of the equation α(x - β)^2 + β(x - α)^2 = 0 are also real and of opposite sign.

If the roots α and β (α + β ≠ 0) of the quadratic equation ax^2 + bx + c = 0 are real and of opposite sign. Then show that roots of the equation α(x - β)^2 + β(x - α)^2 = 0 are also real and of opposite sign. 

Grade:12

1 Answers

mycroft holmes
272 Points
7 years ago
Product of roots is 
 
This immediately means that both roots are real and of opposite signs 
 
(if they were complex, then they are conjugates and their product is always positive)

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