Suppose 1/(a+bi) is a root of the quadratic equation 10x^2-6x+c=0,
where a and b are 3 and -1 respectively.
Find the value of c. (c is a real constant.)
Quadratic Equation, Plz help
2013-03-15 3:43 am
回答 (1)
2013-03-15 5:51 am
✔ 最佳答案
One of the roots is 1/(3 - i) = (3 + i)/[(3 - i)(3 + i)] = (3 + i)/(9 + 1) = (3 + i)/10.Since unreal roots must be in conjugate, the other root is (3 - i)/10.
Product of roots (3 + i)(3 - i)/100 = 10/100 = 1/10 = c/10, therefore c = 1.
2013-03-14 21:55:25 補充：
You may find the other root by using the sum of roots formula, that is - b/a - 1/(3 - i) = 6/10 - 1/(3 - i).
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