Question

Use the x-intercept method to find all real solutions of the equation.
x3 - 6x2 + 3x + 10 = 0

Answer 1

Answer:

The real solutions of the given equation are -1, 2 and 5.

Step-by-step explanation:

The given equation is

$x^3-6x^2+3x+10=0$

At x=-1, the left hand side and the right hand side of the equation are equal. So, (x+1) is a factor of given equation.

Using long division method, divide $x^3-6x^2+3x+10$ by (x+1).

$(x+1)((x^2 - 7 x + 10)=0$

$(x+1)((x^2 - 5x-2x + 10)=0$

$(x+1)(x-5)(x-2)=0$

Equate each factor equal to 0.

$x=-1,2,5$

It means the graph of $x^3-6x^2+3x+10$ intersect the x-axis at -1, 2 and 5. Therefore the real solutions of the given equation are -1, 2 and 5.