Respuesta :
Answer:
Option (a) is correct.
The system of equation becomes
[tex]y=12x^3-5x\\\\ y=2x^2+x+6[/tex]
Step-by-step explanation:
Given : Equation [tex]12x^3-5x=2x^2+x+6[/tex]
We have to construct a system of equations that can be used to find the roots of the equation [tex]12x^3-5x=2x^2+x+6[/tex]
Consider the given equation [tex]12x^3-5x=2x^2+x+6[/tex]
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 [tex]12x^3-5x=2x^2+x+6[/tex]
becomes,
[tex]12x^3-5x=y=2x^2+x+6[/tex]
Thus, The system of equation becomes
[tex]y=12x^3-5x\\\\ y=2x^2+x+6[/tex]
Option (a) is correct.
The system of equations are [tex]\boxed{y = 12{x^3} - 5x}{\text{ and }}\boxed{y = 2{x^2} + x + 6}[/tex] that can be used to find the roots of the equation [tex]12{x^3} - 5x = 2{x^2} + x + 6.[/tex] Option (a) is correct.
Further explanation:
Given:
The equation is [tex]12{x^3} - 5x = 2{x^2} + x + 6.[/tex]
The options are as follows,
(a). [tex]y = 12{x^3} - 5x{\text{ and }}y = 2{x^2} + x + 6[/tex]
(b). [tex]y = 12{x^3} - 5x + 6{\text{ and }}y = 2{x^2} + x[/tex]
(c). [tex]y = 12{x^3} + 2{x^2} - 4x{\text{ and }}y = 6[/tex]
(d). [tex]y = 12{x^3} + 2{x^2} - 4x + 6{\text{ and }}y = 0[/tex]
Explanation:
The given equation is [tex]12{x^3} - 5x = 2{x^2} + x + 6.[/tex]
Consider the left hand side of the equation [tex]12{x^3} - 5x = 2{x^2} + x + 6[/tex] as y and the right hand side of the equation [tex]12{x^3} - 5x = 2{x^2} + x + 6[/tex] as y.
[tex]\begin{aligned}y&= 12{x^3} - 5x\\y &= 2{x^2} + x + 6 \\ \end{aligned}[/tex]
The equation matches with option (a). Hence, option (a) is correct.
The system of equations are [tex]\boxed{y = 12{x^3} - 5x}{\text{ and }}\boxed{y = 2{x^2} + x + 6}[/tex] that can be used to find the roots of the equation [tex]12{x^3} - 5x = 2{x^2} + x + 6[/tex]. Option (a) is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomials
Keywords: polynomial, solution, linear equation, quadratic equation, system of equations, solution of the equations.
