How do you solve an equation like x^2+3x-4=0

There are many ways of solving this equation, which is called a second order polynomial (where the order describes the highest power of x), let's focus on the most general for now: the quadratic formula. 

For any equation of the form ax2+bx+c=0, we can use this formula to find values of x for which this equation is satisfied. Start by calculating the discriminant of our equation, given by D = b2-4ac. If D is bigger than 0, than we can apply the quadratic formula. In our example, a=1, b=3 and c=-4, which means D=32-(-4*4)=9+16=25, which is bigger than 1, so it works! 

The values of x can then be found using the quadratic formula, 

x1=(-b+(squareroot(D))/(2a)

x2=(-b-(squareroot(D))/(2a)

Notice the difference between those two formulas is the + and - in front of the square root of D. 

For our example, this would give: 

x1=(-3+(squareroot(25))/(2*1)=(-3+5)/2=1

x2=(-3-(squareroot(25))/(2*1)=(-3-5)/2=-4

You can check that this is correct by replacing x with one of your values and verify is does equal 0!

Answered by Victor L. Maths tutor

2553 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Find the roots of the following curve: y = 6x^2 - 4x.


Solve the simultaneous equations: x^2-y=16 and 2y-4=14x


The recommended price of a ladder is £75. The ladder is sold in 2 shops, one with a 30% discount the other with a discount of 2/9. How much is the discount in the two shops and which is cheaper and by how much? Non-calculator


Solve the following simultaneous equations: 4x + y = 14 and 6x - y = 16


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