Page 76 - Elementary Algebra Exercise Book I
P. 76
ELEMENTARY ALGEBRA EXERCISE BOOK I equAtions
Solution: The equation should have two imaginary roots and one real root: a ± bi, c . Vieta’s
√
formulas and the modulus 5 lead to
a + bi + a − bi + c = −2k
(a + bi)(a − bi) +(a + bi)c +(a − bi)c =9
(a + bi)(a − bi)c = −5k
2
a + b 2 =5
⇒
2a + c = −2k
2
2
a + b +2ac =9
2
2
(a + b )c = −5k
2
a + b 2 =5
⇒ a = ±1,b = ±2,c = ±2,k = ±2.
When k =2, the equation becomes x +4x +9x + 10 = 0 and its roots are x = −1 ± 2i, x = −2 .
3
2
2
When k = −2, the equation becomes x − 4x +9x − 10 = 0 and its roots are x =1 ± 2i, x =2.
3
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