Question

Find all the roots of the following equations2x^3+x^2-7x-2=0

Answer 1

Let's begin by listing out the information given to us:

2x³ + x² - 7x- 2 = 0

We will proceed to factorise, we have:

(x + 2)(2x² − 3x - 1) = 0

We will proceed to equate the factors to zero, we have:

x + 2 = 0⇒ x = -2

⇒ x = -2

2x² − 3x - 1 = 0

We will use the quadratic formula, we have:

`\begin{gathered} 2x^(2)-3x-1=0 \\ x=(-b\pm√(b^2-4ac))/(2a) \\ a=2,b=-3,c=-1 \\ x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-1)}}{2(2)} \\ x=\frac{3\pm\sqrt[]{9+8}}{4}=\frac{3\pm\sqrt[]{17}}{4} \\ x=\frac{3\pm\sqrt[]{17}}{4}\Rightarrow x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \\ x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \end{gathered}`