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I'm struggling with quadratic equations

Quadratic equations can be tricky, to begin with, but once you get the hang of them they can become one of the best maths tools on offer to you. All quadratic equations with real roots can be solved with the...
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Answered by Ben W. • Maths tutor
3461 Views

Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.

First, we factor out one (x+1). (1+x)^3 = (x+1)^2(x+1)= Then, we expand using the formula (a+b)^2 = a^2 + 2ab +b^2: =(x^2+2x+1)(x+1)= Then we multiply: = x^3 + 2x^2 + x + x^2 + 2x + 1 We sum the terms with t...
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9073 Views

Find dy/dx of the curve x^3+5xy-2y^2-57=0

3x 2 +5y+5x(dy/dx)-4y(dy/dx)=0 3x 2 +5y=(5x-4y)dy/dx dy/dx=(3x 2 +5y)/(5x-4y)
SP
Answered by Steven P. • Maths tutor
4468 Views

Por or Para

Careful with this very common mistake! It may not seem like it will make a big difference, but it can, in fact completely change the meaning of what you are saying. Por is used for: 1) travel and communicati...
CM
Answered by Charlotte M. • Spanish tutor
4102 Views

When should I use imparfait and passé composé?

Passé composé (AVOIR ou ETRE + participe passé) is used for ponctuel actions in the past which have been ended. Ce matin, j’ai mangé une tartine de pain. On the other hand, imparfait is used for descriptions...
CM
Answered by Charlotte M. • French tutor
3193 Views