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How can you find the coefficients of a monic quadratic when you know only one non-real root?

We know that non-real roots appear in complex conjugate pairs. Hence when we know one root, we know both of them. Then, as we can factorise a quadratic in it's linear factors, we know our quadratic is a cons...
WV
Answered by Ward V. • Maths tutor
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By consdering partial fractions find the integral of (1-x)/(5x-6-x^2) between x = 1 and x = 0, give your answer in an exact form.

The answer is Ln8/9, by first converting (1-x)/(5x-6-x^2) into partial fractions you get 1/(2-x) + 2/(x-3), the next step is a simple integration by inspection followed by log manipulations to get the final ...
OA
Answered by Omar A. • Maths tutor
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Re-arrange (3x+y)/2 = x+z making x the subject.

To make x the subject we want to try to get all the x's on one side of the equals sign! Firstly to get rid of the fraction we multiply both sides by 2, giving 3x+y= 2(x+z). We then expand the brackets on the...
LM
Answered by Lara M. • Maths tutor
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Integrate with respect to x ) dy/dx= 6x^5

The integral of any equation let the example be dy/dx = ax^n The integral of (RHS) dy/dx (because when we integrate we are integrating both sides) is y The integral of (LHS) ax^n is [ax^(n+1)]/[n+1] when int...
NM
Answered by Nojus M. • Maths tutor
5386 Views

Define a surd and find the length of one side of a 50cm^2 square shape in surd form

i. A surd is an irrational number i.e. a non-whole number that can be represented as a square root, cube root etc. ii. If the area of the square shape is 50cm^2, then we know that the length multiplied by th...
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Answered by Andrew B. • Maths tutor
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