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We know in a quadratic x^2 +bx + c = 0, -b/a = α + β and c/a = αβ. 

Therefore, α + β = -(-2k) = 2k, and αβ = k - 1. (Both are divided by the coefficient in front of x which is 1 so can be ignored.<...

Firstly, as with any question, make sure to check your formula book in order to find any relevant equations. In this case, the one most relevant to us is U_n = U₁ + d(n-1).
From...

p(x) = 2x⁵ + x⁴ – 26x³ – 13x² + 72x + 36
i) obtain the sum by using vieta's fomula: for p(x) the sum is hence -b/a hence, sum = -1/2
ii) obtain the ...

The equation of a two-dimensional non-vertical line can easily be determined if its gradient 'm' and a point on the line (x0, y0) is known, using the formula m = (y - y0) / (x - x0). The gradient of the t...

a) u is perpendicular to w, so u • w =0. This means that 23 + 3(-1) + (-1)*p = 0, so 6-3-p=0, hence p=3. b) The magnitude of v ...