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Which of the following is a polynomial with roots: − square root of 5 , square root of 5 , and 3? (6 points)


A) x3 − 3x^2 − 5x + 15
B) x^3 + 2^x2 − 3x − 6
C) x^3 − 2x^2 − 3x + 6
D) x^3 + 3x^2 − 5x − 15

Respuesta :

Riia

Let's check the first polynomial , that is

[tex] P(x)= x^3 -3x^2 -5x+15 [/tex]

We need to factor it first and for that we have to do grouping and factoring .

[tex] P(x) = x^2(x-3)-5(x-3)
\\
P(x) = (x^2 -5)(x-3) [/tex]

TO find the roots, we need to set P(x) to 0, that is

[tex] (x^2 -5)(x-3)=0
\\
x^2 - 5= 0 , x-3 =0
\\
x^2 = 5 , x=3
\\
x = \pm \sqrt{5} , x=3 [/tex]

SO the correct option is A .

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