Consider the quadratic equation

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

2x^2 + kx - 3 = 0

, where

k

is a real parameter. (i) Find the set of all real values of

k

for which the equation has no real roots. (ii) For

k = 8

, determine the roots of the equation and hence obtain the x–intercepts of the graph of

y = 2x^2 + 8x - 3

. (iii) Sketch the graph of

y = 2x^2 + 8x - 3

, clearly marking the vertex and the points where the graph meets the coordinate axes.