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.

Answered by Siobhan G. Maths tutor

4057 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Express the number 252 in terms of its prime factors


Work out the number of green pens in the box. (rest of Q below)


Solve the simultaneous equations 5x+2y=11 and x-y=-2.


There is a quarter circle with radius 8cm, what is the area of the quarter circle. The answer should be given in terms of pi, units are cm^2.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences