QUESTIONS - POLYNOMIALS - COMPLEX ROOTS
QUESTIONS - SUNNY - POLYNOMIALS - COMPLEX ROOTS
QUESTION BY SUNNY
WRITE AS PRODUCT OF 2 QUADRATIC FACTORS
ONE REDUCIBLE AND ANOTHER IRREDUCIBLE
THE POLYNOMIAL
P = X^4+6X^3-6X^2+6X-7
AS REASONED ABOVE POSSIBLE RATIONAL ROOTS ARE + OR - 1 AND 7 .
F(1)= 1+6-6+6-7 = 0….SO X=1 IS A ROOT..X-1=0…X-1 IS A FACTOR.
F(-7) = (-7)^4+6*(-7)^3-6*(-7)^2+6*(-7)-7=0
SO X= -7 IS A ROOT …X+7 = 0 ….X+7 IS A FACTOR
DIVIDING WITH THESE 2 FACTORS …
1) 1+6 -6 +6 -7
0+1+7+1+7
---------------------------
1 +7+1+7+0=REMAINDER
QUOTIENT = X^3 +7X^2 +X +7
-7) 1 +7+1+7
0 -7 +0 -7
------------------------
1 +0 +1 +0 = REMAINDER
QUOTIENT = X^2 +1
HENCE THE 2 QUADRATIC FACTORS ARE
(X^2+1) AND
(X-1)(X+7)= X^2+6X-7
ANOTHER METHOD IS TO LET
P = (X^2+AX+B)(X^2+CX+D)
AND SOLVING FOR A,B,C,D
COMPARING LIKE TERMS AND USING TRIAL & ERROR APPROACH
WE GET A=0,B=1,C=6 AND D=-7
posted by mathsmanagementcommonsense at 1:38 AM
4 Comments:
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