Question 1
2 In this question,k is a constant.
It is given that has roots that are real and distinct.
Find the set of possible values of k .
2 In this question,k is a constant.
It is given that 2x2+(3k−2)x+k=0 has roots that are real and distinct.
Find the set of possible values of k .
(3k−2)2−4(2)(k)[∗0]
Uses b2−4ac
* could be any inequality sign or =9k2−20k+4[∗0]
Correctly simplifies to 3-term quadratic
(9 k-2)(k-2)
FT Factorises or solves their 3-term
quadratic
Critical values 92,2k<92k>2k<92k>2
Mark final answer
Solve the inequality (x+2)(4x−5)⩽0.
−2⩽x⩽45 mark final answer
B1 for the correct critical values
Find the values of the constant k for which the equation (2k−1)x2+6x+k+1=0 has real roots. [5]
Uses b2−4ac: 62−4(2k−1)(k+1). M1
−8k2−4k+40 ∗ 0, where * is = or any inequality sign, or equivalent. M1
Factorises or solves their 3-term quadratic expression or equation for critical values, for example (5+2k)(8-4k). M1
Correct critical values: -2.5, 2. A1
−2.5⩽k⩽2. A1