Question

Which system of equations can you

use to find the roots of the equation
2x3 + 4x2 – x + 5 = –3x2 + 4x + 9?

y = 2x3 + x2 + 3x +5
y =9

y = 2x3 + x2
y = 3x + 14

y = 2x3 + 4x2 – x + 5
y = –3x2 + 4x + 9

Answer 1

c the last one

Explanation:

Answer 2

The answer is y = 2x3 + 4x2 – x + 5 and y = –3x2 + 4x + 9
Roots are both: x=-4, x= -1/2 , x= 1

Proof:

Solve for x over the real numbers:
2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9

Subtract -3 x^2 + 4 x + 9 from both sides:
2 x^3 + 7 x^2 - 5 x - 4 = 0

The left hand side factors into a product with three terms:
(x - 1) (x + 4) (2 x + 1) = 0

Split into three equations:
x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0

Add 1 to both sides:
x = 1 or x + 4 = 0 or 2 x + 1 = 0

Subtract 4 from both sides:
x = 1 or x = -4 or 2 x + 1 = 0

Subtract 1 from both sides:
x = 1 or x = -4 or 2 x = -1

Divide both sides by 2:

Answer: x = 1 or x = -4 or x = -1/2