Moderate -0.3 This is a standard discriminant question requiring students to apply b²-4ac > 0 for distinct real roots, then solve a simple linear inequality. It's slightly easier than average because it's a routine application of a well-practiced technique with straightforward algebra and no conceptual surprises.
The quadratic equation \(3x^2 + 4x + (2k - 1) = 0\) has real and distinct roots.
Find the possible values of the constant \(k\)
Fully justify your answer.
[4 marks]
Question 5:
5 | Forms discriminant – condone one
error in discriminant | AO1.1a | M1 | for distinct real roots, disc > 0
42 −4×3×(2k−1) > 0
16−12(2k−1) > 0
28−24k >0
7
k <
6
States that discriminant > 0 for real
and distinct roots | AO2.4 | R1
Forms an inequality from ‘their’
discriminant | AO1.1a | M1
Solves inequality for k correctly
Allow un-simplified equivalent fraction | AO1.1b | A1
Total | 4
The quadratic equation $3x^2 + 4x + (2k - 1) = 0$ has real and distinct roots.
Find the possible values of the constant $k$
Fully justify your answer.
[4 marks]
\hfill \mbox{\textit{AQA AS Paper 2 Q5 [4]}}