Consider that the roots of a cubic equation with integral coefficients are 2, −1, and 4. Which choice is the cubic equation?

Mathematics

1 answer:

Marina86 [1]4 years ago

6 0

The cubic equation having roots 2, -1 and 4 is $x^3-5x^2+2x+8$

Step-by-step explanation:

The roots of the cubic equation are 2,-1 and 4. We need to find the cubic equation.

If 2,-1 and 4 are roots then:

x=2, x=-1 and x=4

or we can write:

x-2=0, x+1=0 and x-4=0

Multiplying the roots to find the cubic equation:

$(x-2)(x+1)(x-4)\\=(x-2)(x(x-4)+1(x-4))\\=(x-2)(x^2-4x+x-4)\\=(x-2)(x^2-3x-4)\\=x(x^2-3x-4)-2(x^2-3x-4)\\=x^3-3x^2-4x-2x^2+6x+8\\Combining\,\,like\,\,terms:\\=x^3-3x^2-2x^2-4x+6x+8\\=x^3-5x^2+2x+8$

So, the cubic equation having roots 2, -1 and 4 is $x^3-5x^2+2x+8$

Keywords: Solving Cubic Polynomial

Learn more about Solving Cubic Polynomial at:

#learnwithBrainly

You might be interested in

Yi's average for her first 3 tests is 88. what musit she score on her last test to bring her average up to 90

timofeeve [1]

Her average now is 88.
She needs to bring it up to a 90.

Let's start with if she gets a 90.
88 + 90 = 178
178/2 = 89
A 90 would only get her an average of 89, so you need to go higher.

88 + 91 = 179
179/2 = 89.5

88 + 92 = 180
180/2 = 90

She must get at least a 92 to get an average of 90.

6 0

4 years ago

If f(x) = 8 -3 and g(x) = 3x2 + x-6, find (f + g)(x).

Marizza181 [45]

Answer:

Step-by-step explanation:

(f+g)(x) basically means to "ADD" f(x) and g(x).

We have

$f(x)=\frac{x}{2}-3$