2x^-9-3x find sum and zero
Answers
Answer:
Answer:
The zeros of the equation are x=-\frac{3}{2},3x=−
2
3
,3
Step-by-step explanation:
Given : Equation 2x^2-9-3x2x
2
−9−3x
To find : The zeros of the quadratic polynomial and verify the relationship between the zeros and the coefficient ?
Solution :
Quadratic equation 2x^2-3x-9=02x
2
−3x−9=0
On comparing with general equation, a=2,b=-3,c=-9
Applying middle term split,
2x^2-6x+3x-9=02x
2
−6x+3x−9=0
2x(x-3)+3(x-3)=02x(x−3)+3(x−3)=0
(2x+3)(x-3)=0(2x+3)(x−3)=0
(2x+3)=0,(x-3)=0(2x+3)=0,(x−3)=0
x=-\frac{3}{2},x=3x=−
2
3
,x=3
The zeros of the equation are x=-\frac{3}{2},3x=−
2
3
,3
The relationship between the zeros and the coefficient,
Sum of the zeros, \alpha+\beta=-\frac{b}{a}α+β=−
a
b
-\frac{3}{2}+3=-\frac{-3}{2}−
2
3
+3=−
2
−3
\frac{-3+6}{2}=\frac{3}{2}
2
−3+6
=
2
3
\frac{3}{2}=\frac{3}{2}
2
3
=
2
3
Verified.
Product of the zeros, \alpha\beta=\frac{c}{a}αβ=
a
c
-\frac{3}{2}\times 3=\frac{-9}{2}−
2
3
×3=
2
−9
-\frac{9}{2}=-\frac{9}{2}−
2
9
=−
2
9
Verified.
Step-by-step explanation:
hope it helps