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Solve 5x-2=3x+11

5x-2=3x+11 Move the (-2) to the right handside. As it crosses over the (-) becomes a (+) 5x=3x + (11+2) Move the (+3x) to the left handside. As it crosses over the (-) becomes a (+) (5x-3x)=(11+2) Complete t...
TF
Answered by Tom F. • Maths tutor
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Find the four complex roots of the equation z^4 = 8(3^0.5+i) in the form z = re^(i*theta)

We know that z=re^(i theta) from the definition of the exponential form of a complex number. Hence it follows that: z^4=(re^(i theta))^4=r^4 e^(4 i theta) We can find z^4 by converting 8(3^0.5+i) (cartesian ...
GG
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Consider f(x)=a/(x-1)^2-1. For which a>1 is the triangle formed by (0,0) and the intersections of f(x) with the positive x- and y-axis isosceles?

We'll first compute these intersections by setting x=0 and y=0 consecutively. This gives y=a-1 and a/(x-1)^2-1=0. Hence we find (x-1)^2=a, so x=1+-sqrt(a). As we have a>1 and we want the intersection with...
WV
Answered by Ward V. • Maths tutor
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What is the largest positive integer that always divides n^5-n^3 for n a natural number.

First we note we can factorise the n^3 out of the expression, giving n^3(n^2-1). Secondly, we can see that the second term is a difference of two squares, allowing is to factorise the total to n^3(n-1)(n+1)....
WV
Answered by Ward V. • STEP tutor
6224 Views

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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