Find the zeroes of the following quadratic
polinomials and verify the relationship between
the coefficients: 6x² -3-7x.
Answers
(a) Let us first find the zeroes of the given polynomial 6x
2
+5x−1 by equating it to 0 as shown below:
6x
2
+5x−1=0
⇒6x
2
+6x−x−1=0
⇒6x(x+1)−1(x+1)=0
⇒(6x−1)(x+1)=0
⇒(6x−1)=0,(x+1)=0
⇒6x=1,x=−1
⇒x=
6
1
,x=−1
Therefore, the zeroes are
6
1
and −1.
In the polynomial 6x
2
+5x−1, we have a=6,b=5 and −1. Now, consider
Sum of zeroes
6
1
+(−1)=
6
1
−1=
6
1−6
=−
6
5
=−
a
b
Product of zeroes
6
1
×(−1)=−
6
1
=
a
c
Hence, the relation between the zeroes and coefficients is verified.
(b) Let us first find the zeroes of the given polynomial 11x
2
−8x−3 by equating it to 0 as shown below:
11x
2
−8x−3=0
⇒11x
2
−11x+3x−3=0
⇒11x(x−1)+3(x−1)=0
⇒(11x+3)(x−1)=0
⇒(11x+3)=0,(x−1)=0
⇒11x=−3,x=1
⇒x=−
11
3
,x=1
Therefore, the zeroes are −
11
3
and 1.
In the polynomial 11x
2
−8x−3, we have a=11,b=−8 and −3. Now, consider
Sum of zeroes
−
11
3
+1=
11
−3+11
=
11
8
=−
11
(−8)
=−
a
b
Product of zeroes
−
11
3
×1=−
11
3
=
a
c
Hence, the relation between the zeroes and coefficients is verified.
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