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

Mathematics

2 answers:

kirill [66]3 years ago

8 0

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.

3241004551 [841]3 years ago

7 0

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.

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