Question

2. Find the roots of 3x^2 – 2x – 5 = 0

Answer 1

The roots are;

`x\text{ = }(5)/(3)\text{ and x = -1}`

Here, we want to find the roots of the given trinomial

To do this, we need to rewrite the middle term (-2x)

This can be obtained by finding the product of the first and last ; the two factors will give this product while the sum of the two factors will be the middle term

Rewriting this mathematically, we have;

`\begin{gathered} 3x^2+3x-5x-5\text{ = 0} \\ so\text{ these two factors are 3x and -5x} \\ \text{Thus, we have;} \\ 3x^2+3x-5x-5\text{ = 0} \\ 3x(x+1)-5(x+1)\text{ = 0} \\ (3x-5)(x+1)\text{ = 0} \\ 3x-5\text{ = 0 or x + 1 = 0} \\ x\text{ = }(5)/(3)\text{ or x = -1} \end{gathered}`