Find the roots of the quadratic equation 2x^2 - 15x - 8
First we have to multiply 8 and 2 together to get 16. We then need to find all the factors for this number.These are:1 and 162 and 84 and 4 From these sets of factors, we have to find which has a difference equal to the middle term of 15. From the pairs of numbers we can see that this is 1 and 16. Finally, we have to find out how we can put these numbers together to make -15. This means making one of them a negative. We can find this to be -16 and 1. From there we can change the equation into 2x2 + x - 16x - 8. To factorise the equation we need to split the whole equation and then find common factors. We can split the equation into 2x2 + x and then -16x - 8. We then need to find a common factor for each side. For the first half, x is found in both 2x 2+ x so we can take it out and make x(2x + 1). We repeat this with the second half to find that -8 can be taken out of both sides of it to make -8(2x + 1). This then makes the entire equation x(2x+1) - 8(2x+1). We can take (2x+1) as a factor for both sides of the equation which leaves us with (x-8)(2x+1).To find the roots, we have to set the equation equal to 0 to make 2x2 - 15x - 8 = 0 or (x-8)(2x+1)=0. For the equation to equal 0 , one or both of the brackets must be zero. The first bracket is equal to 0 when x is equal to 8. The second bracket is equal to zero when x is equal to -1/2. Therefore the solutions to the question are x = 8 and x = -0.5.To double check your answers, you can put them back into the original equation to see if it equals zero.
