Question

Which system of equations can be used to find the roots of the equation 12 x 3-5x=2 x 2+x+6

Answer 1

Answer:

Option (a) is correct.

The system of equation becomes

$y=12x^3-5x\\\\ y=2x^2+x+6$

Step-by-step explanation:

Given : Equation  $12x^3-5x=2x^2+x+6$

We have to construct a  system of equations that  can be used to find the roots of the equation $12x^3-5x=2x^2+x+6$

Consider the given equation $12x^3-5x=2x^2+x+6$

To construct a system of equation put both sides of the given equation equal to a same variable.

Let the variable be "y", Then the equation $12x^3-5x=2x^2+x+6$

becomes,

$12x^3-5x=y=2x^2+x+6$

Thus, The system of equation becomes

$y=12x^3-5x\\\\ y=2x^2+x+6$

Option (a) is correct.

   

Answer 2

The system of equations are $\boxed{y = 12{x^3} - 5x}{\text{ and }}\boxed{y = 2{x^2} + x + 6}$ that can be used to find the roots of the equation $12{x^3} - 5x = 2{x^2} + x + 6.$ Option (a) is correct.

Further explanation:

Given:

The equation is $12{x^3} - 5x = 2{x^2} + x + 6.$

The options are as follows,

(a). $y = 12{x^3} - 5x{\text{ and }}y = 2{x^2} + x + 6$

(b). $y = 12{x^3} - 5x + 6{\text{ and }}y = 2{x^2} + x$

(c). $y = 12{x^3} + 2{x^2} - 4x{\text{ and }}y = 6$

(d). $y = 12{x^3} + 2{x^2} - 4x + 6{\text{ and }}y = 0$

Explanation:

The given equation is $12{x^3} - 5x = 2{x^2} + x + 6.$

Consider the left hand side of the equation $12{x^3} - 5x = 2{x^2} + x + 6$ as y and the right hand side of the equation $12{x^3} - 5x = 2{x^2} + x + 6$ as y.

$\begin{aligned}y&= 12{x^3} - 5x\\y &= 2{x^2} + x + 6 \\ \end{aligned}$

The equation matches with option (a). Hence, option (a) is correct.

The system of equations are $\boxed{y = 12{x^3} - 5x}{\text{ and }}\boxed{y = 2{x^2} + x + 6}$ that can be used to find the roots of the equation $12{x^3} - 5x = 2{x^2} + x + 6$. Option (a) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomials

Keywords: polynomial, solution, linear equation, quadratic equation, system of equations, solution of the equations.