Question

Help me pls w dis question

Answer 1

x = 2 and x = 5

Explanation:

What are the roots of an equation?

In simple terms, the roots are simply the x intercepts of an equation.

How to find the roots of a quadratic equation:

We can find the roots of a quadratic equation one of three ways. Here you will learn how to do all three ways.

The first way (easiest way) :

The first way to find the roots of a quadratic equation is to graph the equation on a calculator and find where the equation crosses the x axis ( these are the x intercepts )

If you look at the attached image, you see the given equation x² - 7x + 10 = 0 graphed. The equation passes the x axis at (2,0) and (5,0) meaning the roots are x = 2 and x = 5.

Second way : Using the quadratic formula:

If you don't have a calculator or don't know how to graph the equation this is the best alternative way to find the roots.

The quadratic formula is :
`(-b\pm√(b^2-4(a)(c)) )/(2(a))`

Where the values of a,b and c are derived from the quadratic equation which should be written in quadratic form : ax² + bx + c = 0

This is the case here so we can easily define our variables and plug them into our formula

We have "ax² + bx + c = 0" = x² - 7x + 10 = 0 so we can say a = 1 , b = -7 and c = 10

We now plug these into the formula

Recall formula :
`(-b\pm√(b^2-4(a)(c)) )/(2(a))`

==> plug in a = 1 , b = -7 and c = 10

`(-(-7)\pm√((-7)^2-4(10)(1))) )/(2(1))`

==> remove parenthesis from -(-7)

`(7\pm√((-7)^2-4(10)(1))) )/(2(1))`

==> simplify exponents

`(7\pm√((49-4(10)(1))) )/(2(1))`

==> simplify all multiplication

`(7\pm√(49-40) )/(2)`

==> subtract 40 from 49

`(7\pm√(9) )/(2)`

==> simplify sqrt

`(7\pm3 )/(2)`

==> simplify +/-

`(7+3 )/(2),(7-3 )/(2)\\(10 )/(2),(4 )/(2)`

==> simplify division

5 , 2

The roots are x = 5 and x = 2

( Note that we used BPEMDAS to evaluate the formula when the values of a,b and c were plugged in. BPEMDAS is simply folllowing an order of operations to ensure you get the right answer. The order is as follows : Brackets , Parenthesis (any operations inside of parenthesis) , Exponents , Multiplication and Division ( do in order going left to right ) , Addition and Subtract ( do in order going left to right )

Also note that the quadratic formula ALWAYS WORKS.

Last way: Factoring

Finally, we can also find the roots by factoring.

We have x² - 7x + 10 = 0

We must first find a number that multiplies to 10 and adds to -7

We can do so by listing the factors of 10

Factors of 10 include , 10 and 1 , -10 and -1 , -5 and -2, and 5 and 2

Out of these we want to find the multiples that add to -7

10 + 1 = 11

-10 + -1 = -11

-5 + - 2 = -7

5 + 2 = 7

The multiples that add to -7 are -5 and -2 .

From there we want to split the -7 and x² to get (x-5)(x-2)

We then solve the roots by setting the individual factors to 0

x - 5 = 0

==> add 5 to both sides

x = 5

x - 2 = 0

==> add 2 to both sides

x = 2