Solve x^2+x-30=0
To solve this question we need to factorise x2 +x-30=0 to find the points in which the function x2 +x-30=0 intersects/ cuts the x axis. We factorise the function x2 +x-30=0 by assessing the function, if the function is a quadratic ie. the highest power of x is 2 we know that there will be 2 solutions in the form of (x+a)(x+b) where a or b could be positive or negative. If the function had a higher power of x say x3 there would be 3 solutions and x4 would have 4 solutions and so on.When finding a and b we look at the integer (number) that is not multiplied by any x and is just a integer in this case 30 and we look at the factors of 30 which are 1,2,3,5,6,10,15,30. Out of these factors we find a pair of factors which multiply together to make 30 and make the coefficient of x which is 1 in this case as is we expand (x+a)(x+b) = x2+ax+bx+ab hence we need a+b=1 and axb=-30. Out of the factors of 30 we can see that 6-5=1 and (-5)x6 = -30 so a and b must be 6 and -5. Hence, x2 +x-30=0 is factorised to (x-5)(x+6)=0.
