Finding a quadratic equation given its two roots. Does this method exist?Quadratic equation given roots:1−23, 1+23

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Finding a quadratic equation given its two roots. Does this method exist?Quadratic equation given roots:1−23, 1+23

xcentricccrhb1 · Accepted Answer

Step 1The important thing about your method isn&#039;t that you have a radical, it&#039;s that you know the number directly between the two roots and the distance from each of the roots to that center number. You can solve your example problem in the same way. If the roots are 2 and -3, you can rewrite these two roots as−12±52 (−12 is directly between 2 and -3 and a distance of 52 from both). Then we can solve the same way you did:x=−12±52x+12=±52(x+12)2=(52)2(x+12)2−(52)2=0So your quadratic equation is f(x)=(x+12)2−(52)2As other people are pointing out, the more obvious answer is f(x)=(x−2)(x+3), but my method is how you can generalize the technique you provided. Note that both methods are equivalent, as (x+12)2−(52)2 can be rearranged to get (x−2)(x+3)

bondsk384r · Accepted Answer

Step 1Sum and product of roots are 2, -11 respectively.x2−2x−11=0;x=1±23 which roots come from (x−1)2=12

Finding a quadratic equation given its two roots.

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