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Oliga [24]
3 years ago
8

Which of the following is a polynomial with roots

Mathematics
2 answers:
PtichkaEL [24]3 years ago
5 0
a(x-x_1)(x-x_2)(x-x_3)\\\\x_1=-\sqrt3;\ x_2=\sqrt3;\ x_3=-2;\ a=1\\\\subtitute\\\\(x+\sqrt3)(x-\sqrt3)(x+2)=(x^2-3)(x+2)\\\\=\boxed{x^3+2x^2-3x-6}\to\fbox{B.}
Anuta_ua [19.1K]3 years ago
5 0
<span> the polynomial has the factor (x-n) </span>
<span>So any polynomial with these roots, must have the factors (x+sqrt(3))(x-sqrt(3))(x+2) </span>
<span>Since these are cubic polynomials (highest x term is x^3), these are all the factors, so the polynomial is of the form: </span>
<span>k(x+sqrt(3))(x-sqrt(3))(x+2) </span>
<span>And since the x^3 term is 1, the constant k must be 1. </span>

<span>So, the polynomial must be the one which is equal to: </span>
<span>(x+sqrt(3))(x-sqrt(3))(x+2) </span>
<span>Since the constant term (the last term) is different for each of your 4 options, you just need to evaluate the constant term and see which one matches. </span>
<span>i.e. the answer is whichever polynomial has a constant term equal to </span>
<span>sqrt(3) times (-sqrt(3)) times 2</span>
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