Question

The line joining the points A(2, t) and B(7, 2t²+ 7)
has a gradient of 2. Find the possible values of t.​

Answer 1

$2 = \frac{2 {t}^{2} + 7 - t}{7 - 2}$

$10 = 2 {t}^{2} - t + 7$

$2 {t}^{2} - t - 3 = 0$

$t = \frac{1 \pm \sqrt{1 + 24} }{4}$

$t = \frac{1 \pm5}{4}$

$\implies \boxed{t = - 1 \: \: or \: \: \frac{3}{2}}$