The required roots of the equation [tex]F(x)=x^3+2x^2-11x-12[/tex] is -1, -4, and 3.
Given that,
[tex]F(x)=x^3+2x^2-11x-12[/tex]
The root of the above polynomial function is to be determined.
What is the equation?
The equation is the relationship between variables and represented as y = ax + c is an example of a polynomial equation.
What is a polynomial function?
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here, In order to find out the root of the equation, we have to factorize the given polynomial function,
Let, [tex]x^3+2x^2-11x-12 = 0[/tex]
[tex]x(2^2+ 2x - 11) - 12=0\\x(x^2 + 2x + 1 - 1 - 11) -12=0\\x[(x+1)^2 - 12] - 12 = 0\\x(x+1)^2-12x - 12=0\\x(x+1)^2 -12(x+1)= 0\\(x+1)(x^2 + x -12)=0\\(x+1)(x^2+4x-3x-12)=0\\(x+1)(x+4)(x-3)=0[/tex]
Now,
x + 1 = 0 ; x + 4 = 0 ; x - 3 = 0
x = -1 ; x = -4 ; x = 3
Thus, the required roots of the equation [tex]F(x)=x^3+2x^2-11x-12[/tex] is -1, -4, and 3.
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