Question 1094973: if the sum of the roots of 2x^2 -3cx + 2x +c^2 = 0 equals the product of roots, what are the possible values of c Answer by ikleyn(52781) (Show Source):
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if the sum of the roots of 2x^2 -3cx + 2x +c^2 = 0 equals the product of roots, what are the possible values of c
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Let me re-write the given equation in an equivalent form
= 0.
Then, according to Vieta's theorem,
- the sum of the roots is equal to = the coefficient at "x" taken with the opposite sign and divided by the leading coefficient,
and
- the product of the roots is equal to = the constant term divided by the leading coefficient.
Therefore, the condition says and directly required that
= , or, equivalently,
= 0.
After factoring left side c^2 - 3c + 2 = (c-1)*(c-2) you easily find the roots c= 1 and c= 2.
Answer. The values of "c" under the question are c= 1 and c= 2.
