A quadratic equation with roots -1 and 4 is -

Explanation

Let $\alpha = -1$ and $\beta = 4$ ∵ $(\alpha + \beta) = -1 + 4 \Rightarrow 3$ $\alpha . \beta = -1 \times 4 = -4$ ∵ Equation $\Rightarrow x^2 - (\alpha + \beta)x + \alpha . \beta = 0$ ∴ Equation $\Rightarrow x^2 - 3x - 4 = 0$ ∵ The sum of 14 terms of the arithmetic progression = 1050 ∴ $S_{14} = 1050$ n = 14 ∵ $S_n = \frac{n}{2} [2a + (n - 1)d]$ ∴ $S_{14} = \frac{14}{2} [2 \times 10 + (14 - 1)d]$ $1050 = 7 (20 + 13 d)$ $150 = 20 + 13d$ $130 = 13d$ d = 10 ∵ From $T_n = a + (n - 1) d$ ∴ The 20ᵗʰ term of the arithmetic progression $T_{20} = 10 + (20 - 1) \times 10$ = $10 + 19 \times 10$ = $10 + 190$ = 200