Multiple choice

Find a quadratic equation formed by using the equations x + y = 5 and xy = 6.

  1. y2– 5y – 6 = 0

  2. y2 + 5y + 6 = 0

  3. y2 – 5y + 6 = 0

  4. y2 + 5x – 6 = 0
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C Correct answer
Explanation

If x and y have sum 5 and product 6, then y satisfies the quadratic t^2 - (sum)t + product = 0. Hence the equation is y^2 - 5y + 6 = 0.

AI explanation

Using the relation between roots and coefficients, if the sum of the roots is 5 and the product is 6, the quadratic equation is t2 - (sum)t + (product) = 0. Substituting the given values results in y2 - 5y + 6 = 0.

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