Use of quadratic formula rather than by factoring

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enelson

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Equation:
2x(squared) + 3x - 4 = 0

An engineer chooses to solve the equation above by using the quadratic formula rather than by factoring. Which of the following facts best explains this choice?

A. The expression 3squared - 4 (2)(4) is negative.

B. Only 3 is odd while 2 and -4 are even.

C. The expression 3squared -4 (2)(-4) is not a perfect square.

D. Only one of the factor pairs of -4 adds to 3.

The answer is C but I am not sure why. If you can explain it to me, it would be great.
Thanks
 
C: If it's a perfect square, it can be factored. If it's NOT a perfect square, it cannot be factored using only integers.
 


We can type exponent notation using the caret symbol ^ (it's a shifted 6, on most keyboards).

I hope that you recognize the given expression 3^2 - 4(2)(-4) as that part of the Quadratic Formula which appears inside the radical sign.

There is a name for the expression b^2 - 4ac

We call it "the discriminant".

As tkhunny wrote, if the discriminant is a perfect square, then the polynomial factors with integer coefficients.



Here is some extra info about the discriminant (beyond this exercise):

If the discriminant > 0, there are two Real solutions for x

If the discriminant = 0, there is one Real solution for x

If the discriminant < 0, there are no Real solutions for x


Cheers 8-)

 
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