Given roots 1 and −3 for a monic quadratic, find the polynomial.
Solution
Correct Answer: Option C
Since the polynomial is monic and its roots are \(1\) and \(-3\), it factors as
\[
p(x)=(x-1)(x-(-3))=(x-1)(x+3).
\]
Expanding,
\[
p(x)=x^2+3x-x-3=x^2+2x-3.
\]
Thus the correct choice is Option 3: \(x^2+2x-3\).
\[
p(x)=(x-1)(x-(-3))=(x-1)(x+3).
\]
Expanding,
\[
p(x)=x^2+3x-x-3=x^2+2x-3.
\]
Thus the correct choice is Option 3: \(x^2+2x-3\).
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