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nataly862011 [7]
3 years ago
8

Use the quadratic formula to solve the equation x^2-7x-6=0

Mathematics
2 answers:
Marysya12 [62]3 years ago
7 0

The roots of the equation {x^2} - 7x - 6 = 0 are x = \dfrac{{7 + \sqrt {73} }}{2}{\text{ or   }}x = \dfrac{{7 - \sqrt {73} }}{2}.

Further explanation:  

The quadratic equation are those equation whose degree is 2.

The general quadratic equation can be expressed as,

a{x^2} + bx + c = 0  

Here, a,b{\text{ and }}c are the real numbers.

The roots of the quadratic equation can be found by the quadratic rule.

x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}  

In the above formula {b^2} - 4ac denotes the discriminant.

Therefore, the value of the discriminant cannot be negative because negative value does not exist in the square root for the real numbers.

The negative value in the root is defined only for the complex numbers.

Given:

The given equation is {x^2} - 7x - 6 = 0.

Step by step explanation:

Step 1:

The given equation {x^2} - 7x - 6 = 0  is the quadratic equation as its degree is 2.

Now to solve the given quadratic equation {x^2} - 7x - 6 = 0 by the quadratic rule we need to find the value of the coefficients and constants.

Now compare the given quadratic equation with general quadratic equation to obtain the value of the coefficients and constant as,

a = 1,b =  - 7,c =  - 6  

Step 2:

Now substitute the value of a = 1,b =  - 7,c =  - 6 in the quadratic formula to obtain the roots of the equation.

\begin{aligned}x &= \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} \hfill \\x &= \frac{{ - \left( { - 7} \right) \pm \sqrt {{{\left( { - 7} \right)}^2} - 4\left( 1 \right)\left( { - 6} \right)} }}{{2\left( 1 \right)}} \hfill \\x &= \frac{{7 \pm \sqrt {49 + 24} }}{2} \hfill \\ x&= \frac{{7 \pm \sqrt {73} }}{2} \hfill \\\end{aligned}  

The above equation can be further solved as,

\begin{aligned}x &= \frac{{7 \pm \sqrt {73} }}{2} \hfill \\x &= \frac{{7 + \sqrt {73} }}{2}{\text{ or   }}x&= \frac{{7 - \sqrt {73} }}{2} \hfill \\\end{aligned}  

Therefore, the roots of the equation {x^2} - 7x - 6 = 0 are x = \dfrac{{7 + \sqrt {73} }}{2}{\text{ or   }}x = \dfrac{{7 - \sqrt {73} }}{2} .

Learn more:  

  1. Learn more about the function is graphed below brainly.com/question/9590016
  2. Learn more about the symmetry for a function brainly.com/question/1286775
  3. Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Quadratic equation

Keywords: linear equation, roots, solution, quadratic equation, coefficients, constants, real number, defined, complex numbers, substitution, general solution, degree, quadratic rule

olganol [36]3 years ago
4 0

Answer:

\frac{7\pm\sqrt{73}} {2}

Explanation:

We have been given with the quadratic equation x^2-7x-6=0

We have general formula to find the roots of a quadratic equation first we find the discriminant with formula

D=b^{2}-4ac

and after that to find the variable suppose x we have the formula

x=\frac{-b\pm\sqrt{D}} {2a}

And general quadratic equation is

ax^2+bx+c=0

On comparing the given quadratic equation with genral quadratic equation we will have values

a=1, b=-7 and c=-6

After substituting these values in the formula we will get  

D=(-7)^2-4(1)(-6)={73}

After substituting in the formula to find x we will get

\frac{-(-7)\pm\sqrt{73}} {2}= \frac{7\pm\sqrt{73}} {2}

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The domain: -5 < x ≤ 1 and the range: -3 ≤ y ≤ 1 is a function. b)

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<h3>What is the domain and range of the function?</h3>

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The domain of a relation is the set of values of the independent variable for a defined function.

The domain is the horizontal extent of the graph.

The range of a relation is the set of values of the dependent variable for a defined function.

The range is the vertical extent of the graph.

The vertical line can intersect the graph in at most one place.

a)

This graph extends from x > -5 to x = 1.

The domain

 -5 < x ≤ 1   ------   (-5, 1] in interval notation

This graph extends from y = -3 to y = 1.

The left side of the graph does not include the point (-5, 1), but the right side includes the point (1, 1).

y = 1 is one of the output values of the relation.

The range

 -3 ≤ y ≤ 1 . . . . . . . . [-3, 1] in interval notation

b)

No, the vertical line crosses the graph in more than one place, therefore, the relation shown is a function.

Learn more about the domain and range of the function:

brainly.com/question/2264373

#SPJ1

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