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f(x)=x^2+12x+32=0, solve for x

Method 1: Quadratic formulaf(x)= ax 2 +bx+c, therefore a=1, b=12, c=32 - quadratic formula= (-b+/-(b 2 -4ac) 1/2 )/2ax=(-12+(144-128) 1/2 /2 = -4 or x=(-12-(144-128) 1/2 )/2 = -8 Method 2: FactoriseWe need t...
Answered by • Maths tutor
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Find the coordinates of the sationary points on the curve x^2 -xy+y^2=12

To find stationary points, we need to find dy/dx and set it equal to 0. Here we must use implicit differentiation: d/dx(x 2 ) + d/dx(-xy) + d/dx(y 2 ) = d/dx(12). Hence 2x - x(dy/dx) - y + 2y(dy/dx) = 0. Fac...
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Answered by Adam B. • Maths tutor
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f(x) = x^3+2x^2-x-2 . Solve for f(x) = 0

f(x) = x 3 + 2x 2 - x - 2 Use the factor theorem to test for f(1) = 0 f(1) = 1 3 + 2*1 2 - 1 - 2 = 0 Therefore x = 1 is a solution and (x-1) is a factor of f(x) Now factorise f(x) x 3 + 2x 2 - x - 2 = (x-1)(...
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Answered by Elena S. • Maths tutor
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If y=2x+4x^3+3x^4 and z=(1+x)^2, find dy/dx and dz/dx.

Differentiation dy/dx = 2+12x^2+12x^3 Chain ruleu = 1+xz=u^2dz/dx = dz/du * du/dx = 2u * 1 = 2(1+x)
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solve this simulatneous equations (with clear algebraic working) : 5x-2y = 33 , 5x + 8y = 18

5x -2y = 33 (substract) 5x + 8y = 18 -10y = 15 y = -1.5 5x + 8(-1.5) = 18 5x = 30 x= 6
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Answered by Lara E. • Maths tutor
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