Question

the sum of a number and twice its square is 105 find the number​

Answer 1

Step-by-step explanation:

Let the required number be x:

Therefore, according to the given information:

$x + 2 {x}^{2} = 105 \\ or \\ 2 {x}^{2} + x = 105 \\ 2 {x}^{2} + x - 105 = 0 \\ 2 {x}^{2} - 14x + 15x - 105 = 0 \\ 2x(x - 7) + 15(x - 7) = 0 \\ (x - 7)(2x + 15) = 0 \\ x - 7 = 0 \: or \: 2x + 15 = 0 \\ x = 7 \: or \: x = - \frac{15}{2} \\ \because x \neq \: - ve \: number \\ hence \: x = 7 \\ \therefore 2 {x}^{2} = 2 \times {7}^{2} = 2 \times 49 = 98 \\ verification \\ x + 2 {x}^{2} = 7 + 98 = 105$