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The cubic polynomial f(x) is defined by f(x) = 2x^3 -7x^2 + 2x + 3. Given that (x-3) is a factor of f(x), express f(x) in factorised form.

f(x) = (x-3)(2x^2 - x - 1)f(x) = (x-3)(2x +1)(x-1)x = 3, -1/2, 1 are roots of the cubic equation.

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How do you prove by contradiction the irrationality of surds. Use sqrt 2 as an example.

Proof by contradiction works by working of the assumption a statement is true, then showing it contradicts with a known truth. It's easy to rote learn the main ones required for Maths A Levels (irriationa...

Answered by • Maths tutor

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X=4x^2 + 5x^7 - sin(3x) find dy/dx

X= 8x+ 35x^6 -3cos(3x)

Answered by Zainab A. • Maths tutor

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Given that x = 4sin(2y + 6), Find dy/dx in terms of x

x = 4sin(2y + 6)dx/dy = 4(2)cos(2y + 6)dx/dy = 8cos(2y + 6) ==> dy/dx = 1/8cos(2y + 6)sin²(2y + 6) + cos²(2y + 6) = 1cos(2y + 6) = √(1 - sin²(2y + 6))cos(2y + 6) = √(1 ...

Answered by Shubham P. • Maths tutor

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Find the area under the curve y=xexp(-x)

first recognise ‘area under’ = integrationfunction is a product so by partsset x=u; exp(-x)=dv/dx integral(udv/dx)=uv-integral(vdu/dx)
du/dx =1; v=-exp(-x)ans=(x.-exp(-x))-integral(1.exp(-x)dx)ans=-x...

Answered by • Maths tutor

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