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Suppose we know that the polynomial equation 4x^3 − 12x²+3x +5 =0 has three real solutions and that one of the factors of 4x^3 − 12x²+ 3x+5 is (x − 1). How can we find all three solutions to the given equation?

Respuesta :

Answer:

So three solution of the equation are x = 1 , 2.5, -0.5

Step-by-step explanation:

We have given equation [tex]4x^3-12x^2+3x+5[/tex]

We have given that (x-1) is a factor of this polynomial so it will completely divide the polynomial

So after division [tex]\frac{4x^3-12x^2+3x+5}{x-1}=4x^2-8x-5[/tex]

So two other factor of polynomial will be the root of [tex]4x^2-8x-5[/tex]

[tex]4x^2-8x-5=(x-2.5)(x+0.5)[/tex]

So three solution of the equation are x = 1 , 2.5, -0.5

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