Question

Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

Answer 1

Answer:

Step-by-step explanation:

Hello,

We need to solve the following equation:

$3x^2 + 5x-8 = 0 \\ \\\text{*** divide by 3 ***}\\\\x^2+\dfrac{5}{3}x-\dfrac{8}{3}=0$

It means that the sum of the zeros is  $-\dfrac{5}{3}$ and the product is $-\dfrac{8}{3}$.

We can easily see that  1 and $-\dfrac{8}{3}$  does the job.

So the solutions are 1 and $-\dfrac{8}{3}$.

Another way to see it is to notice that 1 is a trivial solution as 3+5-8=0, so (x-1) is a factor and (we match the terms)

$3x^2 + 5x-8 = (x-1)(3x+8)=0$

And we find again the same solutions.

Or we use the discriminant.

$x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}=\dfrac{-5-11}{6}=-\dfrac{8}{3}\\\\x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}=\dfrac{-5+11}{6}=1$

The discriminant method works in all cases, so you cannot be wrong using it.

The first method based on the sum and the product usually works well for integer solution which is not the case here.

Finding a trivial solution to be able to factorise could be used here as 1 is really a trivial solution.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you