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Solve x^2 +11x +30 = 0

This is what we call a quadratic equation. To solve, first we need to factorise this equation into two brackets. (x + _ )(x + _) =0To fill the brackets, we need to find 2 numbers that add to 11 and multip...

Answered by Holly R. • Maths tutor

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Find a local minimum of the function f(x) = x^3 - 2x.

To find a local minimum (i.e. a point where the function changes from a negative slope into a positive slope), we first need to find all points where the slope of the function is zero. The first derivativ...

Answered by Karoline H. • Maths tutor

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The equation of line A is (x)^2 + 11x + 12 = y - 4, while the equation of line B is x - 6 = y + 2. Find the co-ordinate(s) of the point at which lines A and B intersect.

While this question may seem complicated, this question is simply asking you to solve the equations of these two lines as simultaneous equations. Line A: x² + 11x + 12 = y - 4 --> x

Answered by Ann A. • Maths tutor

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Solve the following quadratic equation: 2x^2 - 5x - 3 = 0

Firstly, we need to factorise the equation:We can see (and are told) that the equation is quadratic and is therefore of the form ax^2 + bx + c. In our case, a=2, b=-5 and c=-3. We therefore expect two pai...

Answered by Jacob A. • Maths tutor

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The equation " x^3-3x+1=0 " has three real roots. Show that one of the roots lies between −2 and −1

A simple way to prove this is to sub in the values that we are given. so f(x) will represent our equation x^3-3x+1 (that is f(x) = x^3-3x+1)f(-2) = -1 < 0f(-1) = 3 > 0The first thing we notice is th...

Answered by James B. • Maths tutor

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