Jo wants to work out the solutions of x^2 + 3x – 5 = 0. Can the solution be worked out?

In this question we are looking for a solution to x where the equation will equal to 0.We can first try factorising this, in the framework: (x+a)(x+b). Remembering the method of FOILS (first, outer, inner, last and simplify). From this, we know that (bx + ax) must equal 3x. And, (ab) must equal 5. The only integer (whole number) solution to ab = 5 is 5 and 1. Through trial and error, we can find that neither of these combinations can solve (a + b) = 3. We can then deduce this cannot be factorised.Advanced: to know if there is a non-integer answer to this, we can use the quadratic formula. Working through this formula, there is no answer for this either. We don't have to work through the whole formula because we can find that b² - 4ac is a negative number.