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Solve the simultaneous equations: x^2 + 8x + y^2; x - y = 10.

Label the two equations. x 2 + 8x + y 2 = 84 (1) x - y = 10 (2) Rearrange (2) to get y = x - 10 and substitute for y in (1) to get x 2 + 8x + (x - 10) 2 = 84. Expanding and collecting like terms gives 2x 2 -...
LT
Answered by Lewis T. • Maths tutor
5806 Views

What is the binomial theorem and why is it true?

The binomial theorem is an algebraic formula for the expansion of powers of an expression with two terms (a binomial). For example, we can use it to calculate the polynomial expansion of, say, (1+x)^n for an...
JC
Answered by Jacob C. • Maths tutor
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A curve C has the equation x^3 +x^2 -10x +8. Find the points at which C crosses the x axis.

Factorise: (x-2)(x+4)(x-1) Set equal to 0: (x-2)(x+4)(x-1) = 0 Points are (2,0) (-4,0) (1,0)
WF
Answered by William F. • Maths tutor
3827 Views

How to plot quadratic functions, e.g. F(x)= x^2 + 2x +1

What we require to plot this graph are the following: the general shape of the graph, the intercepts with the x and y axes and the maximum point/minimum point. All functions with x 2 as the highest order are...
AS
Answered by Alexandra S. • Maths tutor
6915 Views

How do you solve simultaneous questions?

When an equation has two or more variables, for example and x and y, more than one equation is need to solve it. The number of equations needs is equal to the number of variables you have. For example, if yo...
ES
Answered by Elise S. • Maths tutor
4186 Views