The solutions of the quadratic equation
are
and
.
Further explanation:
The general form of the quadratic equation is given by,
![a{x^2} + bx + c](https://tex.z-dn.net/?f=a%7Bx%5E2%7D%20%2B%20bx%20%2B%20c)
Here,
is the coefficient of
,
is the coefficient of
and
is the constant term.
Given:
Quadratic equation is
.
The options of the solutions of the quadratic equation are
,
,
,
,
and
.
Calculation:
The solution of the quadratic is the value of the variable at which the value of the polynomial is zero.
A polynomial with degree
is a quadratic equation. The quadratic equation has only two solutions.
The polynomial with degree
has
solution.
Solve the given quadratic equation to obtain the solution of the equation.
![\begin{gathered}{\left( {x + 3} \right)^2} = 49 \\x + 3 = \sqrt {49} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%7B%5Cleft%28%20%7Bx%20%2B%203%7D%20%5Cright%29%5E2%7D%20%3D%2049%20%5C%5Cx%20%2B%203%20%3D%20%5Csqrt%20%7B49%7D%20%5C%5C%20%5Cend%7Bgathered%7D)
Take the square root of
to obtain the value of
.
The values of
are
and
.
Now solve the equation to obtain the value of
.
![\begin{gathered}x + 3 = 7{\text{ and }}x + 3 =- 7 \\ x = 7 - 3{\text{ and}{\text{ }}x =-7-3\ \\ x = 4{\text{}}{\text{ and}}{\text{ }}x =-10\, \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7Dx%20%2B%203%20%3D%207%7B%5Ctext%7B%20and%20%7D%7Dx%20%2B%203%20%3D-%207%20%5C%5C%20x%20%3D%207%20-%203%7B%5Ctext%7B%20and%7D%7B%5Ctext%7B%20%7D%7Dx%20%3D-7-3%5C%20%5C%5C%20x%20%3D%204%7B%5Ctext%7B%7D%7D%7B%5Ctext%7B%20and%7D%7D%7B%5Ctext%7B%20%7D%7Dx%20%3D-10%5C%2C%20%5C%5C%20%5Cend%7Bgathered%7D)
The values of
are
and
.
Therefore, the solutions of the quadratic equation are
are
and
.
Learn more:
1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Quadratic equation
Keywords: quadratic equation, polynomial, square root, solutions, zeroes, variable, degree, real numbers, coefficients, constant term, general form of quadratic equation.