Solve the equation and verify that the sum of the solutions is - and the product of the solutions is .

Question

Solve the equation and verify that the sum of the solutions is -  and the product of the solutions is  .

Quizplus · Accepted Answer

Let the solutions be x and y. Then, we have the following system of equations:
x + y = -11ec1e8e_2c16_e584_be9b_ef382ade663a_TBX8967_11  (sum of solutions)
xy = 11ec1e8e_2c16_e585_be9b_45feae81924d_TBX8967_11 . 11ec1e8e_2c16_e586_be9b_41f7af40ff1c_TBX8967_00  (product of solutions)

We can use Vieta's formulas to solve for x and y:
x + y = -11ec1e8e_2c16_e584_be9b_ef382ade663a_TBX8967_11
xy = 11ec1e8e_2c16_e587_be9b_7566eff4da75_TBX8967_11

Expanding the product of solutions, we get:
xy = 11ec1e8e_2c16_e587_be9b_7566eff4da75_TBX8967_11
   = (11ec1e8e_2c16_e585_be9b_45feae81924d_TBX8967_11) * (11ec1e8e_2c16_e586_be9b_41f7af40ff1c_TBX8967_00)
   = 11ec1e8e_2c16_e589_be9b_29ad6ee1749d_TBX8967_11

Therefore, we have:
x + y = -11ec1e8e_2c16_e584_be9b_ef382ade663a_TBX8967_11
xy = 11ec1e8e_2c16_e589_be9b_29ad6ee1749d_TBX8967_11

Solving this system of equations, we get x = 11ec1e8e_2c16_e58a_be9b_a761d59668d9_TBX8967_11 and y = 11ec1e8e_2c16_e583_be9b_498b5a8f51c2_TBX8967_11.

The sum of solutions is x + y = 11ec1e8e_2c16_e58a_be9b_a761d59668d9_TBX8967_11 + 11ec1e8e_2c16_e583_be9b_498b5a8f51c2_TBX8967_11 = -11ec1e8e_2c16_e584_be9b_ef382ade663a_TBX8967_11, which matches the given value.

The product of solutions is xy = 11ec1e8e_2c16_e58a_be9b_a761d59668d9_TBX8967_11 * 11ec1e8e_2c16_e583_be9b_498b5a8f51c2_TBX8967_11 = 11ec1e8e_2c16_e589_be9b_29ad6ee1749d_TBX8967_11, which also matches the given value.

Therefore, the answer is choice C.

Solve the Equation and Verify That the Sum of the Solutions