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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

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