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!

VL
Answered by Victor L. Maths tutor

2809 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is the probability that the next baby born in England will be a boy?


The perimeter of a right angled triangle is 105cm. The lengths of its sides are in the ratio of 2:6:7. Work out the area of the triangle.


The line l is a tangent to the circle x^2 + y^2 = 40 at the point A. A is the point (2,6). The line l crosses the x-axis at the point P. Work out the area of the triangle OAP.


What is the value of x if (15*sqrt(x)) / sqrt(5) = 6*sqrt(5)


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences