The roots of the equation (V - W)X2 + (W - U)X + (U - V) = 0 are:
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1 , V − U V − W
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1 , U − V V − W
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− 1 , V − W V − U
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− 1 , W − U V − W
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− 1 , V − U U − W
Reveal answer
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B
Correct answer
Explanation
The equation is (V-W)X^2 + (W-U)X + (U-V) = 0. Notice the sum of coefficients: (V-W) + (W-U) + (U-V) = 0. If the sum of coefficients is 0, then X=1 is a root. The product of roots is (U-V)/(V-W). Since one root is 1, the other root is (U-V)/(V-W).
AI explanation
We can check that x = 1 is a root by substituting it into the equation, which yields (V - W) + (W - U) + (U - V) = 0. For the second root, we divide the polynomial by (x - 1) to get (V - W)x - (V - U) = 0. Solving this linear equation gives x = (V - U) / (V - W), which equals (U - V) / (W - V). The roots are 1 and (U - V) / (W - V).