Find the zeroes of the polynomial f(x)=x3−8x2+19x−12,if it is given that the product of its two zereoes is 4.
A
3,4 and 2
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B
3,4 and 1
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C
3,2 and 1
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D
3,1 and 7
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Solution
The correct option is B
3,4 and 1 Let zeroes of f(x)=x3−8x2+19x−12beα.βandγ.αβ=4αβγ=−da=−(−12)1=12⇒4γ=12⇒γ=124=3∴(x−3) is a factor of f(x) x3−8x2+19x−12⇒(x−3)(x2−5x+4)⇒(x−3)(x2−4x−x+4)⇒(x−3)[x(x−4)−1(x−4)]⇒(x−3)(x−4)(x−1)Zeroes of f(x) are 3, 4, and 1
So, the correct option is b