Question

What is the polynomial function of lowest degree with rational real coefficients and roots 2 and squared root 5?

Answer 1

The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0

The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be

(x - 2) (x - √5) (x + √5) = 0

(x - 2) (x² - 5) = 0

x³ - 5x - 2x² + 10 = 0

=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.

Learn more about Polynomial at:

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