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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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Hey please help me please help please
Airida [17]

1.

a) metres to centimetres :

multiply length by 100

b) metres to millimetres:

multiply length by 1000

c) kilograms to grams:

multiply the mass value by 1000

d) litres to millilitres :

multiply volume by 1000

2.

a) 3 m = 3× 100 = 300 cm

b) 28 cm = 28 × 10 = 280 mm

c) 2.4 km = 2.4 × 1000

= 24 × 10^-1 × 10^3

= 24 × 10^2 =2400 m

d) 485 mm =485 / 10

= 485 / 10 ^1

= 485 × 10 ^-1

= 48.5 cm

e) 35 cm = 35 / 100

= 35 /10^2

= 35 × 10 ^ -2

= 0.35 m

f) 2.4 m = 2.4 / 1000

= 24 × 10 ^-1 / 10^3

= 24 × 10^-1 × 10 ^-3

= 24 × 10 ^ -4

= 0.0024 km

g) 2495 mm = 2495 /1000

= 2495 /10^ 3

= 2495 × 10 ^-3

=2.495 m

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