the two digit number is obtained by either multiplying the sum of digits by 8 and then subtracting 5 or by multiplying different digit by 16 and adding 3 find the number
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Step-by-step explanation:
We have,
p(x)=3x
3
−5x
2
−11x−3
And the zeros are
3,−1,
3
−1
Verifying the zeros,
x=3,p(3)=3(3)
3
−5(3)
2
−11(3)−3
=81−45−33−3
=0
=x−1,p(−1)=3(−1)
3
−5(−1)
2
−11(−1)−3
=−3−5+11−3
=0
x=
3
−1
,
p(
3
−1
)=3(
3
−1
)
3
−5(
3
−1
)
2
−11(
3
−1
)−3
9
−1
−
9
5
+
3
11
−3
9
−1−5−33−27
0
Now verifying the relation between zeros and coefficients is:
for,
p(x)=3x
3
−5x
2
−11x−3
a=3,b=−1,c=−11,d=−1
and zeros α=3,β=−1γ=
3
−1
Now,
α+β+γ
=3+(−1)+
3
−1
=
3
9−3−1
3
5
=
a
−b
αβ+βγ+γα
=(3)(−1)+(−1)(
3
−1
)+(
3
−1
)(3)
3
−9+1−3
=
3
−11
=
a
c
αβγ
=(3)(−1)(
3
−1
)
1=
a
d
Thus the relation are verified.
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