Number Theory/factors

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Question
pls find the factors of 3x^2+12x-2511=0.stepwise answer would be helpful.

Answer
Hello Mick

The quadratic has numerical factor 3, so it becomes:
3(x^2 + 4x -837) = 0.
We now need factors of 837 which differ by 4.  These must be close to the square root of 837 which is close to 29.  This suggests the factors of 837 required are 27 and 31.  Using a factor tree on 837 =3*837 = 3*3*93 + 3*3*3*31 confirms this.
So we end up with 3(x+31)(x-27) = 0.  I'm sure you can now solve the equation.

Best wishes

vijilant

Number Theory

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Vijilant

Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

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