A polynomial equation with rational coefficients has the roots 7 +square root 3, 2 –square root six. Find two additional roots.
(1 point)
Responses
7 –square root 3, 2 +square root six
7 – Image with alt text: square root 3 , 2 + Image with alt text: square root six
3 –square root 7, 6 +square root two
3 – Image with alt text: square root 7 , 6 + Image with alt text: square root two
7 +square root 3, 2 –square root six
7 + Image with alt text: square root 3 , 2 – Image with alt text: square root six
3 + square root 7, 6 –square root two
3 + Image with alt text: square root 7 , 6 – Image with alt text: square root two
Whats the right answer
The right answer is:
7 - √3, 2 + √6
The two additional roots of the polynomial equation are 7 - √3 and 2 + √6.
The correct answer is 7 - √3 and 2 + √6.
To find the additional roots, we know that for a polynomial equation with rational coefficients, complex conjugate pairs are roots. This means that if a + bi is a root, then its conjugate, a - bi, is also a root.
Given that the given roots are 7 + √3 and 2 - √6, their conjugates are 7 - √3 and 2 + √6. So, the two additional roots are 7 - √3 and 2 + √6.