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

Last updated date: 21st Mar 2023

•

Total views: 305.7k

•

Views today: 2.84k

Answer

Verified

305.7k+ views

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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE