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Solve equation 1/x + x^3 + 5x=0

For x!=0, multiply the equation by x to get x^4+5x^2+1=0. Then substitute t=x^2 where t>=0. So the equation has a form t^2+5t+1. Then find the discriminant and two roots. One of the roots t2<0 doesn't ...
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Answered by Jakub O. • Maths tutor
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Is a line ax+by+c=0 tangent to a circle?

Get a line a form y=-ax/b-c/b, then substitute into a cirle equation (x-p)^2 +(y-s)^2=r^2. Get a quadratic and find whether a discriminant is equal to zero. If it is then the line is tangent to a circle. Oth...
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Answered by Jakub O. • Maths tutor
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How do you find the prime factorisation of a large number like 420?

You start by dividing 420 by whichever numbers you know that it is divisible by. 420 is obviously divisible by 10 so you can start with 10 x 42. Then, you factorise 10 and 10 = 2 x 5, so now we know 420 = 2 ...
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Answered by Abisayo A. • Maths tutor
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How do you solve the simultaneous equation, 7x – 20 = 3x + 4?

To solve this equation we want to find the value of one unknown, x. The solution will be x = ___. So first we need to put all the terms with x on one side of the =, and all the constants on the other side. T...
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Answered by Abisayo A. • Maths tutor
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Pythagoras: If you have a right angled triangle PQR, and length PQ=5cm, length QR=8cm (which is the longest length), then calculate length PR to two decimal places.

Pythagoras' theorem is: a^2+b^2=c^2 (a=short side, b=short side, c=longest side/hypotenuse, ^=squared). Now applying that to this question would mean that a=PQ, b=PR and c=QR. So we can use the figures given...
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Answered by Pree S. • Maths tutor
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