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The equation 3x^2 – 5x + 4 = 0 has roots P and Q, find a quadratic equation with the roots (P + 1/2Q) and (Q + 1/2P)

We know the roots of the equation 3x 2 - 5x + 4 = 0 is P & Q, therefore is is equivalent to (x - P)(x - Q) = 0. Expanding the expression we get x 2 - x(P+Q) + PQ = 0 . Equating coefficents with the origi...
SC
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Find the General Second Order Differential Equation Using Substitution (A2 Further Maths)

Find the General Second Order Differential Equation 4x 2 d 2 y/dx 2 - 8x dy/dx +(8+4x 2 )y = x 4 , Transform Using y = vx. 1) Differentiate both sides of y = vx (apply Product Rule to right hand side) dy/dx ...
SC
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Solve this equation: x^2 + 2x + 2

x = (-2 +/- sqrt(4-8))/2 therefore x = - 1 +/- i, where i is the imaginary unit
AE
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Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions

x = i is a solution, and all the coefficients are real, so x = -i must also be a solution:2x^3+3x^2+2x+3 = 0(x+i)(x-i)(Ax+B) = 0 (we argued above that this must be the case)(x^2+1)(Ax+B) = 0(x^2+1)(2x+3) = 0...
BS
2510 Views

Let Curve C be f(x)=(1/3)(x^2)+8 and line L be y=3x+k where k is a positive constant. Given that L is tangent to C, find the value of k. (6 marks approx)

SO when we see the word tangent we should be thinking about rate of change. Recall that the line being a tangent means they meet and have the same derivative at this point OR we find k such that f(x)-y=0 has...
GJ
8445 Views