a)By completing the square, prove the quadratic formula starting from ax^2+bx+c=0, b) hence, or otherwise solve 3x^2 + 7x -2= 9, to 3s.f.

a)starting from ax2+bx+c=0, divide through by a, x2+(b/a)x+c/a=0, complete the square (x+(b/2a))2-(b/2a)2 +c/a=0, expand (x+(b/2a))2-(b2/4a2)+c/a=0, Combine fractions and rearrange,(x+(b/2a))2=(b2-4ac)/4a2, square root both sides, x+b/2a=±√(b2-4ac)/2a, minus b/2a from both sides and obtain quadratic formula of x=(-b±√(b2-4ac))/2a.
b)3x2 + 7x -2= 9, to use quadratic formula, equation must equal 0, 3x2 + 7x -11=0 , x=(-7±√(72-43-11))/2*3 =1.08 or -3.41 (3s.f.)

YH
Answered by Yusuf H. Maths tutor

3244 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Make x the subject of the formula y = x/3 -2a


Prove that the difference between the squares of two consecutive odd numbers is a multiple of 8.


Solve the quadratic equation x^2 + x - 6 = 0


Simplify fully: (24 - √ 300)/(4√ 3 - 5). Give your answer in the form a√ b where a and b are integers and find the values of a and b.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences