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If the roots of the quadratic equation 1/2*x^2 + 99x + c = 0 are x = -99 + sqrt(8021) and x = -99 - sqrt(8021), then what is the value of c?

 May 18, 2022
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Recall the quadratic formula: \(\large{x = {-b \pm \sqrt{b^2-4ac} \over 2a}}\).

Subsituting in what we know, we get: \(\large{{-99 \pm \sqrt{8021}} = {-99 \pm \sqrt{99^2-4\times{1 \over 2}c} \over 2\times {1 \over 2}}}\)

Notice the discriminant (\(b^2 - 4ac\)). It must equal 8021, because the denominator is 1. 

 

This means that we can derive the equation: \(99^2 - 2c = 8021\)

 

Now, we have to solve for c. 

 

Can you take it from here?

 May 18, 2022

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