roots of quadratic equations: verify for 2x^2 - 5x + 7 = 0

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Jodene222

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Cliff solved the equation 2x^2 - 5x + 7 = 0 and noticed that the sum of the roots was 5/2 and the product of the roots was 7/2. Solve the equation and verify Cliff's results.

I have used the quadratic equation a = 2; b = -5; c = 7

I get 5.57 and 0.16
 
Re: roots of quadratic equations

Really? That quadratic doesn't have any real roots.

\(\displaystyle x = \frac{5 \pm \sqrt{25 - 4(2)(7)}}{2(2)}\)

\(\displaystyle x = \frac{5 \pm \sqrt{-31}}{4}\)

Now you have two non-real roots. All you have to do is add them and multiply them to see if they agree with Cliff's answers.
 
Re: roots of quadratic equations

You don't have to actually. Just leave the negative sign in there and see what happens when you add and multiply the two roots.
 
Re: roots of quadratic equations

That is the same answer I get. The square root of -31 is 5.57i. The sum of the roots is supposed to equal 5/2.
 
Re: roots of quadratic equations

Yes, but that's not a root of the quadratic. We said that the roots were:
\(\displaystyle \frac{5 + \sqrt{-31}}{4}\)
(which is approximated to be 1.25 + 1.39i)

and

\(\displaystyle \frac{5 - \sqrt{-31}}{4}\)
(which is approcimated to be 1.25 - 1.39i)
Add them to see what you get. And multiply them to see what you get and you'll find that they do indeed agree with Cliff's answers.

Edit: Forgot to divide root(31) by 4
 
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