Answer

Verified

338.4k+ views

**Hint:**Here, we will remove the brackets and gather all the like terms and add or subtract them in order to get only a single term with a particular variable. By solving this further using mathematical operation, we will be able to find the required sum of the given two quadratic equations. Hence, this will be the required answer.

**Complete step-by-step answer:**

In order to find the sum of the given two quadratic equations, first of all, we will remove the parentheses as they are unnecessary and do not impact the question.

Thus, we get,

\[\left( {4{x^2} - 6x + 7} \right) + \left( { - 19{x^2} - 15x - 18} \right) = 4{x^2} - 6x + 7 - 19{x^2} - 15x - 18\]

Now, we will gather the like terms and solve them further by adding or subtracting whatever the case is.

\[ \Rightarrow \left( {4{x^2} - 6x + 7} \right) + \left( { - 19{x^2} - 15x - 18} \right) = \left( {4{x^2} - 19{x^2}} \right) + \left( { - 6x - 15x} \right) + \left( {7 - 18} \right)\]

\[ \Rightarrow \left( {4{x^2} - 6x + 7} \right) + \left( { - 19{x^2} - 15x - 18} \right) = - 15{x^2} - 21x - 11\]

**Therefore, the required value of \[\left( {4{x^2} - 6x + 7} \right) + \left( { - 19{x^2} - 15x - 18} \right)\] is \[ - 15{x^2} - 21x - 11\]**

Hence, this is the required answer.

Hence, this is the required answer.

**Additional information:**

In this question, we removed the parentheses. Parentheses are a pair of curved marks or brackets that we put around words or numbers to indicate that they are additional, separate, or the sign between them shows that the equations in the parentheses are being added, subtracted, divided or multiplied. Thus, it plays a vital role in the separation of two or more equations.

**Note:**

Quadratic equations are the polynomial equations of a second degree. This means that they contain at least one variable with a power or exponent two. The solutions of the quadratic equations are the values of unknown variables \[x\], which satisfies the equation. There are two possible solutions or roots of the quadratic equations. The number of solutions of an equation is equal to the highest degree of the equation.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Which places in India experience sunrise first and class 9 social science CBSE

The list which includes subjects of national importance class 10 social science CBSE

What is pollution? How many types of pollution? Define it

State the laws of reflection of light