Solve. x2 - χ - 6 = 0 A.{2,-3} B.{-2, -3} C.{3, -2} D.{6, -1}
Mathematics · Middle School · Thu Jan 21 2021
Answered on
Given the quadratic equation:
x^2 - x - 6
a = 1
b = -1
c = 6
Determine the values of x.
Solution:
In order to solve for the roots of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -1 since the middle value is -x which is the same as having 1 as the numerical coefficient, and when multiplied, the answer is -6. Hence, if we are unable to find the number, we will use the quadratic formula.
The given numbers that satisfy this conditions are { 3 -2}.
(x - 3)(x + 2)
In order to check if the numbers are 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 to the first term of the second equation.
=(x)(2)
= 2x
First term of the first equation multiplied to the last term of the second equation.
=(-3)(x)
=-3x
Last term of the first equation multiplied to the first term of the second equation.
=(-3)(2)
= -6
Last term of the first equation multiplied to the fast term of the second equation.
= x^2 + 2x - 3x - 6
= x^2 - x - 6
Final answer:
{ 3, -2}