A polynomial equation with rational coefficients has the roots 7 + * sqrt * 3, 2 - * sqrt * 6. Find two additional roots.

a. 7 - * sqrt * 3, 2 + * sqrt * 6

b. 3 - * sqrt * 7, 6 + * sqrt * 2

c. 7 + * sqrt * 3, 2 - * sqrt * 6

d. 3 + * sqrt * 7, 6 - * sqrt * 2

Question

Giselle Taylor

Mathematics

28 September, 07:55

A polynomial equation with rational coefficients has the roots 7 + * sqrt * 3, 2 - * sqrt * 6. Find two additional roots.

a. 7 - * sqrt * 3, 2 + * sqrt * 6

b. 3 - * sqrt * 7, 6 + * sqrt * 2

c. 7 + * sqrt * 3, 2 - * sqrt * 6

d. 3 + * sqrt * 7, 6 - * sqrt * 2

+1

Answers (1)

Know the Answer?

Gummi Bear · Answer 1

If the coefficients of a polynomial equation are rational, then the irrational roots have to come in conjugate pairs.

The conjugate of 7 + √ 3 is 7 - √ 3 and the conjugate of 2 - √ 6 is 2 + √ 6.

Answer:

A) 7 - √ 3, 2 + √ 6

A polynomial equation with rational coefficients has the roots 7 + * sqrt * 3, 2 - * sqrt * 6. Find two additional roots.a. 7 - * sqrt * 3, 2 + * sqrt * 6b. 3 - * sqrt * 7, 6 + * sqrt * 2c. 7 + * sqrt * 3, 2 - * sqrt * 6d. 3 + * sqrt * 7, 6 - * sqrt * 2

A polynomial equation with rational coefficients has the roots 7 + * sqrt * 3, 2 - * sqrt * 6. Find two additional roots.

a. 7 - * sqrt * 3, 2 + * sqrt * 6

b. 3 - * sqrt * 7, 6 + * sqrt * 2

c. 7 + * sqrt * 3, 2 - * sqrt * 6

d. 3 + * sqrt * 7, 6 - * sqrt * 2