Use algebra to show that the equation 5x(x-3) = 5x-26 has no real solutions.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [M1] 5x² – 20x + 26 [= 0]
2. [M1] Correctly finds b² – 4ac for their 5x² – 20x + 26 [= 0] e.g. (–20)² – 4(5)(26)
3. [A1] 400 – 520 < 0 or –120
4. [(M1)] Condone one slip in expansion of brackets or collection of terms (5x² – 20x + 26 [= 0])
5. [(M1)] Completes the square 5(x – 2)² + 6 and states the correct minimum point (2, 6)
6. [(A1)] Correct conclusion e.g. Minimum point at y = 6 therefore does not intersect x-axis oe