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Solve 3x^2 - 4x - 6 = 0.

The at first can seem very challenging and you won't be able to tackle this question quickly using simple factorisation, which you can often do for many questions. It is best in this case then to use the Qua...
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Answered by Aodhan B. • Maths tutor
5156 Views

Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2

For the first part, use the 'complete the square method', which gives (x-7/2) 2 -49/4+2, simplified to (x-7/2) 2 -41/4. To find the answer for the second part, set x=7/2 so that the bracketed part becomes 0,...
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Answered by Connaire W. • Maths tutor
5313 Views

Find the binomial expansion of (2+x)^3

We know thst the binomial expansion formula is (1+x) n = 1+nx +(n)(n-1)(x 2 )/2! ...etc Thus we want to rearrange the expression we are given into the form (1+x) n so that we can apply the formula to it. Tak...
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Answered by Laura V. • Maths tutor
11349 Views

Given that y = 3x(^2) + 6x(^1/3) + (2x(^3) - 7)/(3(sqrt(x))) when x > 0 find dy/dx

Firstly, the (2x(^3) - 7)/(3(sqrt(x))) can be split into (2x(^3))/(3(sqrt(x)) and -7/(3(sqrt(x)). These can then be simplified to (2/3)x(^5/2) and -(7/3)x(^-1/2) respectively. This then gives the equation y ...
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Answered by Samuel H. • Maths tutor
17620 Views

Solve the following simultaneous equations: 3a + 2b = 36 equation ( 1), and 5a + 4b = 64 equation (2)

This question can be answered by the elimination method, substitution method or graphically. I find the elimination method easiest, especially when you can see that the coefficient of a variable (in this cas...
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Answered by Alejandro G. • Maths tutor
6465 Views