Use of discriminantUse the discriminant to determine the number and type of solutions for the given equation. X^2+ 3x-4=0 I need to see all the steps to get the answer
You need to remember the quadratic formula such that:
You need to identify the coefficients a,b,c such that:
You should know that the radicand is called discriminant since the number of zeroes of quadratic equation depends on the values of radicand.
In this case, evaluating the discriminant yields:
Notice that the positive value of discriminant means the existence of two values for roots of quadratic equation.
Hence, evaluating the roots of the equation yields and
The discriminant of the quadratic is:
delta = b^2 - 4ac
We'll identify the coefficients a,b,c:
a = 1
b = 3
c = -4
We'll calculate delta, by substituting the coefficients:
delta = 9-4*1*(-4)
delta = 9+16
delta = 25
Now, we'll discuss the role of delta when deciding the number of real solutions of the quadratic.
If delta > 0 => the equation has 2 different real solutions.
If delta = 0 => the equation has 2 equal solutions.
If delta < 0=> the equation has no real solutions.
In this case, delta = 25 > 0 => the equtaion has 2 real different solutions:
x1 = (-b+sqrt delta)/2a
x1 = (-3 + sqrt 25)/2
x1 = (-3+5)/2
x1 = 1
x2 = (-3-5)/2
x2 = -4