Question

Form a quadratic polynomial whose zeros are root 5, and the product of the zeroes is -2√5.

Answer 1

A quadratic polynomial with zeros √5 and the product -2√5 is x² + √5x - 2√5 = 0.

Step-by-step explanation:

The question is how to form a quadratic polynomial whose zeros are root 5, and the product of the zeroes is -2√5. Using the fact that a quadratic equation can be expressed in terms of its zeros as ax² - (sum of roots) • x + product of roots = 0, we can construct our polynomial.

If the zeros are √5 and -2√5, then the sum of the roots is (√5 + (-2√5)) = -√5 and the product of the roots is (√5) • (-2√5) = -2√5. Assuming the leading coefficient 'a' is 1 for simplicity, our quadratic polynomial is x² - (-√5)x + (-2√5) = 0 or simply x² + √5x - 2√5 = 0.