# What will be the sum of the roots of quadratic equation $2{x^2} + 4x + 6 = 0$?

Answer

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Hint: In this question we have been given a quadratic equation and we have to find the sum of the roots. Roots of this quadratic equation refers to the values of x which will satisfy the given equation. Use the direct formula of sum of roots which is minus times the coefficient of x divided by the coefficient of highest power term.

Complete step-by-step answer:

Given quadratic equation is

$2{x^2} + 4x + 6 = 0$

Now we have to find out the sum of roots of the quadratic equation.

Let us consider the general quadratic equation,

$a{x^2} + bx + c = 0$

Let the roots of this quadratic equation be${x_1},{\text{ }}{x_2}$.

Now as we know that the sum of the roots of this quadratic equation is $ = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - b}}{a}$

$ \Rightarrow {x_1} + {x_2} = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - b}}{a}$.

Now the given quadratic equation is $2{x^2} + 4x + 6 = 0$

So, on comparing (a = 2, b = 4, c = 6)

Let the roots of this quadratic equation be$\alpha ,\beta $.

So, the sum of the roots of the quadratic equation $ = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - b}}{a}$

$ \Rightarrow \alpha + \beta = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - 4}}{2} = - 2$.

So, the sum of the roots of the quadratic equation is -2.

So, this is the required answer.

Note: Whenever we face such types of problems there are always two methods to find the sum or even the product of the roots. The first one is the formula based approach as mentioned above, the second one involves calculation of the roots of the given quadratic equation using factorization or Dharacharya formula. The later one being length it is always advised to grasp the direct formula to solve such type of problems, it helps saving a lot of time.

Complete step-by-step answer:

Given quadratic equation is

$2{x^2} + 4x + 6 = 0$

Now we have to find out the sum of roots of the quadratic equation.

Let us consider the general quadratic equation,

$a{x^2} + bx + c = 0$

Let the roots of this quadratic equation be${x_1},{\text{ }}{x_2}$.

Now as we know that the sum of the roots of this quadratic equation is $ = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - b}}{a}$

$ \Rightarrow {x_1} + {x_2} = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - b}}{a}$.

Now the given quadratic equation is $2{x^2} + 4x + 6 = 0$

So, on comparing (a = 2, b = 4, c = 6)

Let the roots of this quadratic equation be$\alpha ,\beta $.

So, the sum of the roots of the quadratic equation $ = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - b}}{a}$

$ \Rightarrow \alpha + \beta = \dfrac{{ - {\text{ coefficient of }}x}}{{{\text{coefficient of }}{x^2}}} = \dfrac{{ - 4}}{2} = - 2$.

So, the sum of the roots of the quadratic equation is -2.

So, this is the required answer.

Note: Whenever we face such types of problems there are always two methods to find the sum or even the product of the roots. The first one is the formula based approach as mentioned above, the second one involves calculation of the roots of the given quadratic equation using factorization or Dharacharya formula. The later one being length it is always advised to grasp the direct formula to solve such type of problems, it helps saving a lot of time.

Last updated date: 26th Sep 2023

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