Answer to Question #245319 in Calculus for minu

Question #245319


Let h(x) =f(x)/g(x) where h(x) is polynomial of x. f f(x) = x3-2x2-3x and g(x)=x-3,then find the number of real solutions of the equation h(x)=0 in the interval [-2.0, 2.0]












1
Expert's answer
2021-10-04T16:41:26-0400
h(x)=x32x23xx3=x(x22x3)x3h(x)=\dfrac{x^3-2x^2-3x}{x-3}=\dfrac{x(x^2-2x-3)}{x-3}

=x(x+1)(x3)x3=x(x+1),x3=\dfrac{x(x+1)(x-3)}{x-3}=x(x+1), x\not=3

h(x)=0=>x(x+1)=0,x3h(x)=0=>x(x+1)=0, x\not=3

x1=1,x2=0x_1=-1, x_2=0

There are two real solutions of the equation h(x)=0 in the interval [-2.0, 2.0].



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