Answer:
a)
x -3 -2 -1 0 1 2 3
y 0 8 6 0 -4 0 18
b)
see in the table, at x = {-3; 0; 2}, y = 0
=> x = {-3; 0; 2} is the solutions of the equation x³ + x² - 6x = 0
Step-by-step explanation:
a) 0 and 6 will be written in the given blank spaces.
b) The value of x for the given equation is 0, -3 and 2.
It is a method for finding the values of variable, by substituting the value of one variable to get the another.
To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero.
a). We have, an equation
[tex]y = x^{3}+x^{2} -6x[/tex]
so, at x = -3
[tex]y = -3^{3} +(-3)^{2} -6(-3)[/tex] = -27+9+18 = 0 (substitute x = -3 in the given equation)
at x = -1
y = [tex]-1^{3} +(-1)^{2} -6(-1) = -1+1+6 = 6[/tex]
Hence, 0 and 6 will we written the blank spaces of the given table.
b). We have an equation
[tex]x^{3} +x^{2}-6x = 0[/tex]
⇒ [tex]x(x^{2} +x-6)=0[/tex]
⇒ [tex]x (x^{2} +3x-2x-6)=0[/tex]
⇒ [tex]x(x(x+3)-2(x+3))=0[/tex]
⇒ [tex]x(x+3)(x-2)=0[/tex]
⇒ [tex]x = 0,-3 and 2[/tex]
Hence, 0, -3 and 2 are the solutions of the given equation.
Learn more about substitution method here:
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