Find the discriminant of the equation. x^2 + 3x - 4 = 0
Mathematics · High School · Thu Feb 04 2021
Answered on
Given the numerical equation:
x^2 + 3x - 4
Determine the discriminant.
Solution:
In order to determine the discriminant of the equation, we must simply solve for x. To solve for x , we need look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 3, and when multiplied, the answer is -4. Hence, if we are unable to find the number, we will use the quadratic formula. The factors that satisfy the conditions are,
( x + 4)( x - 1)
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)(-1)
= -x
First term of the first equation multiplied to the last term of the second equation.
=(4)(x)
=4x
Last term of the first equation multiplied to the first term of the second equation.
=(-4)(1)
= -4
Last term of the first equation multiplied to the fast term of the second equation.
= x^2 - x + 4x - 4
= x^2 + 3x - 4
To solve for the discriminant we equate the factors to 0 then solve for x.
x + 4 = 0
x - 1 = 0
Transpose -1 and 4 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
x = -4
x = 1
Final answer:
x = -4
x = 1