find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials: (b) 2s^2-(1+2√2) s+√2
Answers
Answer:
Step-by-step explanation:
Let f(x)=2x
2
+
2
7
x+
4
3
Comparing it with the standard quadratic polynomial ax
2
+bx+c, we get
a=2, b=
2
7
, c=
4
3
Now, 2x
2
+
2
7
x+
4
3
=2x
2
+
2
6
x+
2
1
x+
4
3
=2x(x+
2
3
)+
2
1
(x+
2
3
)
=(x+
2
3
)(2x+
2
1
)
The zeros of f(x) are given by f(x)=0
=>(x+
2
3
)(2x+
2
1
)=0
=>(x+
2
3
)=0 or (2x+
2
1
)=0
=>x=−
2
3
or x=−
4
1
Hence the zeros of the given quadratic polynomial are −
2
3
, −
4
1
Verification of the relationship between the roots and the coefficients
Sum of the roots =(−
2
3
)+(−
4
1
)
=−
4
7
=−
2×2
7
=
coefficientofx
2
−coefficientofx
Product of the roots =(−
2
3
)(−
4
1
)
=−
8
3
=−
4×2
3
=
coefficientofx
2
constantterm