x2+9x+20 plz help with it
Mathematics · High School · Tue Nov 03 2020
Answered on
Given the quadratic equation:
x^2 + 9x + 20
Determine the solution/roots.
Solution:
In order to determine the solution of any given quadratic equation, we must factor out the values of x in the equation. In order to do so, we must look first at the 3rd and 2nd term. The two factors must have the product equal to the third term, and the sum must be equal to the second term. Hence, the two numbers that satisfy the equation are 5 and 4.
(x + 5) ( x + 4)
In order to check if the equation is true we will use the FOIL Method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (x)(x)
=x^2
First term of the first equation multiplied by the first term of the second equation.
=(x)(4)
= 4x
First term of the first equation multiplied by the last term of the second equation.
=(5)(x)
=5x
Last term of the first equation multiplied by the first term of the second equation.
=(5)(4)
= 20
Last term of the first equation multiplied by the fast term of the second equation.
= x^2 + 4x + 5x + 20
= x^2 + 9x + 20
Now that we've determine that (x + 5) (x + 4) is true, we solve for the value of x by equating each factor to 0.
x + 5 = 0
x = -5
x + 4 = 0
x = -4
Final answer:
The solution for the given quadratic equation is
x = -4 and x = -5