Question

If a polynomial function, f(x), with rational coefficients has roots 3 and startroot 7 endroot, what must also be a root of f(x)? negative startroot 7 endroot i startroot 7 endroot –3 3i

1. The root of f(x) will be (A) -√7.

### What is a polynomial function?

• A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
• For example, 2x+5 is a polynomial with an exponent of one.
To find the root of f(x):
• A polynomial function f(x) has roots 3 and √7.
• 3 is a real number.
• √7 is an irrational number.
• The zeros or root of the function always occurs in conjugate pair.
Conjugate pair: A root has two forms one positive and one negative.
Example: a + √b, a – √b
• For the given function f(x), √7 should be in conjugate pair.
• One more possible root would be √7.
Therefore, the root of f(x) will be (A) -√7.
Know more about polynomial functions here:
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The correct question is given below:
If a polynomial function f(x) has roots 3 and a square root of 7 what must also be a root of f(x)?
A. negative square root of 7
B. i square root of seven
C. –3
D. 3i