find the zeros of the following quadratic polynomial and verify the relation between the zeros and the coefficients x²-3x+2
Answers
Answer:
x^2 + 3x + 2 ( let the sum = 3 and product = 2)
a=1, b=3, c=2
α+β= -3
αβ= 2
therefore, x^2 +3x +2=0
= x^2 +2x+x+2=0
= x(x+2) +1(x+2)=0
=(x+1) (x+2) =0
so, the zeros will be:
x=-1 and -2
therefore, the sum of zeros= -1-2=-3
the product of zeros= -1(-2)=2
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Answer:
Here multiple options are correct.
3x
2
−5x−2
and
3x
2
−x
are correct.
A
3x
2
−5x−2=0
2a
−b±
b
2
−4ac
6
5±
25+24
6
5±7
α=2,β=
3
−1
α+β=
a
−b
2
3
−1
=
3
5
3
5
=
3
5
B
9y
2
−6y+1=0
9y
2
−3y−3y+1=0
3y(3y−1)−1(3y−1)=0
(3y−1)(3y−1)=0
y=
3
1
α=
3
1
,β=
3
1
α+β=
a
−b
3
1
+
3
1
=
3
2
αβ=
3
1
3
1
=
9
1
C
4z
2
+12z+9=0
4z
2
+6z+6z=9=0
2z(2z+3)+3(2z+3)=0
(2z+3)(2z+3)=0
y=
2
−3
α=
2
−3
,β=
2
−3
α+β=
a
−b
2
−3
+
2
−3
=
4
−12
−3=−3
Similarly αβ=
a
c
=
4
9
D
3x
2
−x=0
x(3x−1)=0
x=0,
3
1
α=0,β=
3
1
α+β=
a
−b
0+
3
1
=
3
1
3
1
=
3
1
αβ=
a
c
=0