Higher November 2021 Paper 1 Q15
15 \((x + a)(x + 3a) \equiv x^2 + bx + 75\)
Work out the two possible values of \(b\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x^2 + 3ax + ax + 3a^2\) (\(\equiv x^2 + bx + 75\)) or \(x^2 + 4ax + 3a^2\) (\(\equiv x^2 + bx + 75\)) or \(3ax + ax + 3a^2 \equiv bx + 75\) or \(4ax + 3a^2 \equiv bx + 75\) or \(3a^2 = 75\) | M1 | |
| \(a = 5\) and/or \(a = -5\) | A1 | implied by \((x + 5)(x + 15)\) or \((x - 5)(x - 15)\) implied by answer 20 and/or \(-20\) |
| 20 and \(-20\) | A1 | oe \(\pm 20\) |