Given that one root of the equation x3−10x2+31x−30=0 is 5 then other roots are
A
2 and 3
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B
2 and 4
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C
3 and 4
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D
−2 and −3
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Solution
The correct option is A2 and 3 Method I:
Let f(x)=x3−10x2+31x−30=0 ∵f(2)=23−10(2)2+31(2)−30−0 and f(3)=33−10(3)2+31(3)−30=0
So, x=2 & 3 are the other roots of given equation
Method II: x3−10x2+31−30=0 ∴(x−5)(x2−5x+6)=0
or (x−5)(x−3)(x−2)=0 ∴x=5,3,2