if x is equal to minus 1 by 3 is a zero of polynomial p x is equal to 27 x cube minus a x square + X + 4 then find the value of a
Answers
Answer:
Step-by-step explanation:
\text{Given }x=-\frac{1}{3}\text{ is zero of the polynomial P(x) which is }P(x)=27x^3-ax^2-x+3Given x=−
3
1
is zero of the polynomial P(x) which is P(x)=27x
3
−ax
2
−x+3
we have to find the value of a
P(x)=27x^3-ax^2-x+3P(x)=27x
3
−ax
2
−x+3
\text{As }\frac{-1}{3}\text{ is zero of the polynomial therefore by remainder theorem}As
3
−1
is zero of the polynomial therefore by remainder theorem
P(-\frac{1}{3})=0P(−
3
1
)=0
27(-\frac{1}{3})^3-a(-\frac{1}{3})^2-(-\frac{1}{3})+3=027(−
3
1
)
3
−a(−
3
1
)
2
−(−
3
1
)+3=0
27(-\frac{1}{27})-a(\frac{1}{9})+\frac{1}{3}+3=027(−
27
1
)−a(
9
1
)+
3
1
+3=0
-1-\frac{a}{9}+\frac{10}{3}=0−1−
9
a
+
3
10
=0
\frac{a}{9}=\frac{7}{3}
9
a
=
3
7
a=\frac{7}{3}\times 9=21a=
3
7
×9=21
Hence, the value of a is 21