Can you explain the formula method for solving quadratic equations?

We can use the formula method (for solving quadratic equations) to find 'roots' or values of x that satisfy or 'work out' for a given quadratic equation of an unknown variable (say x.) The formula is:x=-b(+or- sqrt[b2-4ac])/2aNote that the 'plus or minus' can give us 2 possible values or 'roots' for the unknown 'x'. These may be 2 positive roots, 2 negative roots, or a negative and a positive root. These roots are the coordinates where a curve/line intersects with the x axis (we know that y=0 on the x-axis already.)We may compare our quadratic equation to the general format (ax2+bx+c) to obtain the values for a, b, and c, which are coefficients of x (c is the coefficient of x0 which equals 1.)Our 2 values may then be substituted back into our original equation to show that the 2 sides 'match' and thus the equation is valid. We let the quadratic equation equal zero to display that the 2 sides are balanced or 'homogeneous'.Example:Solve the quadratic equation 3x2+9x+3 via the formula method.Firstly, we must compare the above quadratic equation with the general format (ax2+bx+c) to obtain values for the coefficients of x. We can see that a=3, b=9, and c=3. Our general formula:x=-b(+or- sqrt[b2-4ac])/2ais thusx=-9(+or- sqrt[(9)2-4(3)(3)])/2(3)So that by solving for x, x=-0.381 (3 d.p.) and x=-2.618 (3 d.p.). We obtained these answers by adding and subtracting the square root terms (respectively) and performing the arithmetic.We can check that these are correct by equating the quadratic to zero and substituting in our x values:3(-0.381)2+9(-0.381)+3=0.00648333(-2.618)2+9(-2.618)+3=-0.000228Thus our roots are correct! The equations do not equal zero exactly as we have rounded our roots to 3 decimal places.

Answered by Daniel M. Maths tutor

6050 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations 2x + y = 7 and 3x - y = 8


How do I solve this linear equation? Angles A and B are in a quadrilateral are in ratio 2:3, angle C is 30 degrees more than angle B and angle D is 90 degrees.


What do I do when quadratic equations aren't written in the standard format ax^2 + bx + c = 0 ?


White paint costs £2.80 per litre. Blue paint costs £3.50 per litre. White paint and blue paint are mixed in the ratio 3 : 2 Work out the cost of 18 litres of the mixture.


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 2013–2024

Terms & Conditions|Privacy Policy