If \((x-1)\) and \((x+3)\) are the factors of \(x^2+k_1x+k_2\), then:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(k_1=2\), \(k_2=-3\)
A quadratic with leading term \(x^2\) and factors \((x-1)\) and \((x+3)\) is the product of the two factors. Comparing coefficients then gives \(k_1\) and \(k_2\).
\((x-1)(x+3)=x^2+3x-x-3=x^2+2x-3\)
Comparing with \(x^2+k_1x+k_2\): \(k_1=2\) and \(k_2=-3\)