Multiple choice

If a and ß are the roots of the equation x2 + px +q = 0, then – a–1, –ß–1 are the roots of which one of the following equations?

  1. qx2 – px + 1 = 0

  2. qx2 + px + 1 = 0

  3. x2 + px – q = 0

  4. x2 – px + q = 0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a and ß are roots of x² + px + q = 0, then a + ß = -p and aß = q. For the new roots -1/a and -1/ß: sum = -(1/a + 1/ß) = -(a+ß)/(aß) = p/q and product = 1/(aß) = 1/q. The equation is x² - (p/q)x + 1/q = 0, which multiplying by q gives qx² - px + 1 = 0. Option B would give x² + (p/q)x + 1/q = 0, which is incorrect.

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