Complete the following table for the Polynomial P(x) = 6x²-13x+6
Answers
Step-by-step explanation:
=
3
2
and \beta=\frac{3}{2}β=
2
3
Step-by-step explanation:
Given : Quadratic polynomial 6x^2-13x+66x
2
−13x+6
To find : The zeros of the quadratic polynomial and verify the relation between the zeros and its coefficients?
Solution :
Quadratic polynomial 6x^2-13x+66x
2
−13x+6
Applying middle split,
6x^2-9x-4x+6=06x
2
−9x−4x+6=0
3x(2x-3)-2(2x-3)=03x(2x−3)−2(2x−3)=0
(3x-2)(2x-3=0(3x−2)(2x−3=0
(3x-2)=0,(2x-3)=0(3x−2)=0,(2x−3)=0
x=\frac{2}{3},x=\frac{3}{2}x=
3
2
,x=
2
3
Therefore, Zeros of the quadratic polynomial is
\alpha=\frac{2}{3}α=
3
2
and \beta=\frac{3}{2}β=
2
3
Now, The relation between zeroes and coefficients is
Sum of zeros is \alpha +\beta=-\frac{b}{a}α+β=−
a
b
Product of zeros is \alpha\times\beta=\frac{c}{a}α×β=
a
c
Where, a=6,b=-13 and c=6
Now, Substitute the values
\frac{2}{3}+\frac{3}{2}=-\frac{13}{6}
3
2
+
2
3
=−
6
13
\frac{4+9}{6}=-\frac{-13}{6}
6
4+9
=−
6
−13
\frac{13}{6}=\frac{-13}{6}
6
13
=
6
−13
Sum of zeros is Verified.
\frac{2}{3}\times\frac{3}{2}=\frac{6}{6}
3
2
×
2
3
=
6
6
\frac{6}{6}=1
6
6
=1
1=11=1
Product of zeros is Verified.
Therefore, The relation is verified
Step-by-step explanation:
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