Derive from the standard quadratic equation, the form of the quadratic solution
ax2+bx+c=0 : basic quadratic equation
a(x2 + bx/a) + c=0
a((x+b/2a)2 - b2/4a2) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b2/4a2, )
a(x+b/2a)2 - b2/4a + c= 0 (a cancels 4a2 to make 4a)
a(x+b/2a)2 = (b2-4ac)/4a (rewrite b2/4a - c)
(x+b/2a)2 = (b2-4ac)/4a2
(x+b/2a) = +/-(rootof(b2-4ac))/2a (square root gives +/- answers
x= (-b +/- (rootof(b2-4ac)))/2a (x term singled out and the quadratic soln is written)
JD
Related Maths A Level answers
All answers ▸A curve has the equation y = 4x^3 . Differentiate with respect to y.
Find the value of: d/dx(x^2*sin(x))
Show that, for all a, b and c, a^log_b (c) = c^log_b (a).
For a graph C with equation y=3/(5-3x)^2, find the the equation of the line normal to the graph at point P, where x=2. Give your answer in the form ax+by+c=0