Question

Find the zeros of the polynomial f(x) = x3 - 12x + 47x - 60, if it is given that sum of its two zeros is 9
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Answer 1

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If the zeroes of the polynomial f(x)=x3−12x2+39x−28 is in A.P,then its zeroes are _____

(A)−7,4,1(B)−7,−4,−1(C)7,−4,1(D)7,4,1

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A)

f(x)=x3−12x2+39x−28

Let a-d, a, a+d be the zeroes of the Polynominal

Sum of Zeroes=−(−121)=12

(i.e) a-d + a + a+d = 12

⟹3a=12ora=4

Product of Zeroes=−(−281)=28

(a-d) (a) (a+d) = 28

a(a2−d2)=28But a=4

(a2−d2)=7

(i.e)16−d2=7⟹d2=9

Therefore d=±3

Hence the roots are:

(3 - 4) (4) (3 + 4) or (-3 - 4) (4) (-3 + 4)

(i.e) -1, 4, 7 or -7, 4, 1