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Solve x^2 + 8x +3 = 0 by completing the square.

Using the completing the square method: 1. Notice (x+4) 2 = x 2 + 8x +16 which differs from the question by a constant 2. So we can write: x 2 + 8x + 3 = (x+4) 2 - 13 (check this yourself if you don't see it...
TD
Answered by Tutor21349 D. • Maths tutor
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Integrate 4x^3 + 6x^2 +4x + 3

Each term is integrated according to the formula: ax b --> (a/(b+1))x (b+1) A constant k integrates to kx Since this is indefinite integration, an additional term of +c must be added to the expression. Th...
EH
Answered by Emma H. • Maths tutor
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Differentiate y = 2x^3 + 6x^2 + 4x + 3 with respect to x.

Each term is differentiated according to the formula: y = ax b --> dy/dx = b*ax (b-1) Constants differentiate to zero. Therefore in this example: dy/dx = 6x 2 + 12x + 4
EH
Answered by Emma H. • Maths tutor
8017 Views

Find the gradient of a curve whose parametric equations are x=t^2/2+1 and y=t/4-1 when t=2

Remember that the gradient of a curve is expressed as dy/dx. This can be solved by using the chain rule: dy/dx = dy/dt*dt/dx. The dt in the denominator of the first term, and the numerator of the second term...
AS
Answered by Abigail S. • Maths tutor
9674 Views

Where does the geometric series formula come from?

Rearranging the terms of the series into the usual "descending order" for polynomials, we get a series expansion of: ax n-1 + ........ax + a A basic property of polynomials is that if you divide x ...
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Answered by Naheem A. • Maths tutor
5183 Views