Multiple choice

If α and β are two roots of the quadratic ax2 – bx + c = 0 where a, b, and c are constants and a ≠ 0, then the value of 1 α + 1 β is

  1. − b c

  2. b c

  3. c a

  4. c b
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B Correct answer
Explanation

For ax^2 - bx + c = 0, sum of roots alpha + beta = b/a, product alpha * beta = c/a. 1/alpha + 1/beta = (alpha + beta) / (alpha * beta) = (b/a) / (c/a) = b/c.

AI explanation

For the quadratic equation ax2 - bx + c = 0, the sum of the roots (alpha + beta) is given by -(-b)/a, which simplifies to b/a. The product of the roots (alpha times beta) is given by c/a. We need to find the value of (1/alpha) + (1/beta), which can be combined into (alpha + beta) divided by (alpha times beta). Substituting the sum and product values gives (b/a) divided by (c/a). The a terms cancel out, leaving b/c.

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