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The quadratic equation 2x^2 + 8x + 1 = 0 has roots x1 and x2. Write down the value of x1+x2 and x1*x2 and find the value of x1^2 + x2^2

If a quadratic equation is of the form : ax^2 +bx +c =0and has roots x1 and x2, then the following statements are true:x1+x2 = - b/ax1x2 = c/aIn our case: x1+x2 = - 8/2 = -4and x1x2 = 1/2Now, x1^...

Answered by Bogdan-Adrian M. • Maths tutor

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If y = 1/(x^2) + 4x, find dy/dx

First, notice that 1/(x^2) = x^(-2)dy/dx = d/dx (x^(-2) + 4x)The derivative of the sum is the sum of the derivatives= d/dx (x^(-2)) + d/dx (4x)The derivative of x^n is nx^(n-1), for every real number n, a...

Answered by Bogdan-Adrian M. • Maths tutor

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Given that (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2) = 7, show that tan(x)^2 = 3/2

First, we use 1 - sin(x)^2 = cos(x)^2 and get:(LHS) (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2)= (cos(x)^2 + 4 sin(x)^2)/cos(x)^2= 1 + 4 (sin(x)/cos(x))^2= 1 + 4 tan(x)^2Now we know that the left hand side is eq...

Answered by Bogdan-Adrian M. • Maths tutor

7266 Views

The surface run-off of nitrate from agricultural fertiliser into freshwater ponds and lakes can cause the death of the fish. Explain how this happens.

This question crops up a lot and may be up to a five mark question, if you learn the key points and terms you can be confident of getting all the marks you can here!