Question

What Should be added to 14x3+29 x² =37x+61
to get 2x² - 10x² + 2x -23.
7​

Answer 1

Answer:

Let the unknown quadratic equation be ax³ + bx² + cx + d

14x³ + 29x² = 37x + 61 ⇒ 14x³ + 29x² - 37x - 61

∴ 14x³ + 29x² - 37x - 61 + (ax³ + bx² + cx + d) = 2x³ - 10x² + 2x -23

⇒ ax³ + bx² + cx + d = 2x³ - 10x² + 2x -23 - (14x³ + 29x² - 37x - 61)

⇒ ax³ + bx² + cx + d = 2x³ - 10x² + 2x -23 - 14x³ - 29x² + 37x + 61

⇒ax³ + bx² + cx + d = -12x³ - 39x² + 39x + 38

∴ (-12x³ - 39x² + 39x + 38) should be added to 14x3+29 x² =37x+61

to get 2x² - 10x² + 2x -23

                        Hope it helps you^_^