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Factorise and solve x^2 - 8x + 15 = 0

In order to solve a quadratic equation by factorisation you must first find the two numbers which add up to - 8 and multiply to get 15. We can do this by trial and error - first listing all of the pairs of f...
LM
Answered by Lucy M. • Maths tutor
5610 Views

Differentiate y = 7(x)^2 + cos(x)sin(x)

This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rule: ...
EC
Answered by Edward C. • Maths tutor
4181 Views

Find the set of values of x for which x(x-4) > 12

When solving this quadratic inequality, we should use a three-step approach. The first step is to reformat the inequality to put one side equal to zero, which is the standard format of a quadratic equation. ...
DB
Answered by Daniel B. • Maths tutor
14624 Views

Simplify (5-2√3)/(√3-1) giving your answer in the form p +q√3, where p and q are rational numbers

The trick here is to use a technique called the difference of squares. If we multiply the top and bottom of the fraction by the conjugate* of the denominator, we can remove any square root terms from the den...
AW
Answered by A W. • Maths tutor
21029 Views

Find the exact solution of the equation in its simplest form: 3^x * e^4x = e^7.

First take natural logs of both sides, giving us: ln(3 x * e 4x ) = ln(e 7 ). The RHS can be simplified using the definition of natural logs, so ln(e 7 ) = 7. We can then apply the product rule for logs (ln(...
HM
Answered by Hugo M. • Maths tutor
5891 Views