Determine whether the equation (4x+1)(3x+2)/(5x-3) = x+1 has two distinct real roots, two equal roots or no real roots.

Mark scheme

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

1. [B2] 7x² +9x+5[=0] or -7x²-9x-5[=0]
2. [B2] B1 for two terms correct in 7x² +9x+5=0 or at most one term incorrect in 12x² +11x+2=5x² + 2x-3 oe
3. [M1] FT their 3-term quadratic
4. [M1] 9²-4(7)(5) or (-9)²-4(-7)(-5) oe
5. [A1] -59 and no real roots or 81-140<0 and no real roots oe
6. [B1] (√x)² + 4√x−12 = 0 oe soi
7. [B1] or y = √x and y² + 4y − 12 = 0 oe soi
8. [M1] Factorises or solves their 3-term quadratic in √x
9. [A2] A1 for √x = 2
10. [A2] A1 for √x = -6
11. [A2] x=8 x=-216