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Find the two real roots of the equation x^4 - 5 = 4x^2 . Give the roots in an exact form. [4]

x⁴ - 5 = 4x². In order to find the roots of this equation we must factorise it, and, to do so, it must be rearranged such that all the terms are on one side. Therefore, subtract 4x

Answered by Sanjay S. • Maths tutor

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Explain the difference between osmosis and diffusion.

Osmosis is the movement of water molecules from an area of high concentration to an area of low concentration, through a partially permeable membrane.Diffusion is the movement of molecules from an area of...

Answered by Alexander R. • Biology tutor

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ABC is an isosceles triangle such that AB = AC A has coordinates (4, 37) B and C lie on the line with equation 3y = 2x + 12 Find an equation of the line of symmetry of triangle ABC. Give your answer in the form px + qy = r where p, q and are integers (5

As we know that AC = AB, then it must be the case that BC is the base of the triangle (because it is isosceles). Therefore, the line of symmetry of the triangle ABC goes through the point A, and is perpen...

Answered by Sanjay S. • Maths tutor

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(i) Identify the ablative absolute and (ii) translate the sentence into good English: 'Urbe capta, hostes cives occiderunt.'

(i) Urbe (3rd declension feminine noun) capta (past participle passive in agreement with urbe). The ablative noun and participle are 'cut off' from the rest of the sentence - if we removed the phrase from...

Answered by Samuel M. • Latin tutor

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