MYTUTOR SUBJECT ANSWERS

192 views

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])/2a

Note 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])/2a

is thus

x=-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=0.0064833

3(-2.618)2+9(-2.618)+3=-0.000228

Thus our roots are correct! The equations do not equal zero exactly as we have rounded our roots to 3 decimal places.

Daniel  M. GCSE Maths tutor, GCSE Physics tutor, GCSE Biology tutor, ...

5 months ago

Answered by Daniel , a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

336 SUBJECT SPECIALISTS

£18 /hr

Billy W.

Degree: Philosophy, Politics & Economics (Bachelors) - Exeter University

Subjects offered: Maths, Religious Studies+ 3 more

Maths
Religious Studies
Philosophy and Ethics
-Personal Statements-

“I am a Philosophy, Politics and Economics first year student at the University of Exeter from Brentwood in Essex. Before university I studied at Westcliff High School for Boys which is an Academy Grammar School in Southend-on-Sea, Ess...”

MyTutor guarantee

£18 /hr

Ruchira R.

Degree: BA English (Bachelors) - Exeter University

Subjects offered: Maths, English Literature+ 2 more

Maths
English Literature
Biology
.ELAT

“About Me I am currently studying English at the University of Exeter. I've taught children from a wide range of age groups before, including my own peers. AS I have studied English, Maths and Biology at A Level and obtained an A in ea...”

£22 /hr

James L.

Degree: Medical Sciences (Bachelors) - Exeter University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Physics
Chemistry
Biology

“Hi, I'm James, a 2nd year Medical Science student. I'm really passionate about science, and I hope i can share some of it with you! ”

About the author

Daniel M.

Currently unavailable: for regular students

Degree: Physics (Bachelors) - Bath University

Subjects offered: Maths, Science+ 4 more

Maths
Science
Physics
Chemistry
Biology
-Personal Statements-

“Hi! I'm Daniel! As a patient, understanding, and industrious tutor, I aim to nourish your child's academic curiosity in a caring, understandable and encouraging manner so that they may be the best that they can be. I'm currently readi...”

You may also like...

Other GCSE Maths questions

How do you find the mean of 5 values?

Sasha has a bag containing 12 red beads, and 8 blue beads. She draws one bead from the bag at random. What is the probability that it is blue?

Solve algebraically 6a + b = 16 and 5a - 2b = 19

What is a good way to remember the sine, cosine and tangent rules of a triangle?

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok