x2+2x+3≡(x+a)2+bx^2 + 2x + 3 \equiv (x + a)^2 + bx2+2x+3≡(x+a)2+b.
Find the values of the constants a a\,a and bbb.
Sketch the graph of y=x2+2x+3y = x^2 + 2x + 3y=x2+2x+3, indicating clearly the coordinates of any intersections with the coordinate axes.
Find the value of the discriminant of x2+2x+3x^2 + 2x + 3x2+2x+3. Explain how the sign of the discriminant relates to your sketch in part (b).
The equation x2+kx+3=0x^2 + kx + 3 = 0x2+kx+3=0, where k k\,k is a constant, has no real roots. Find the set of possible values of kkk, giving your answer in surd form.
Practise Edexcel A Level Old Maths Algebra and Functions 1 with exam-style questions for A Level Old Maths. 19 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.