Find the zeroes of the polynomial f(x)= 2x² - 5x + 3 and verify the relationship between the zeroes and the coefficients.
Answers
ANSWER
We have,
f(x)=x
2
−2
=x
2
−(
2
)
2
=(x−
2
)(x+
2
)
The zeroes off(x) are given by f(x)=0
(x−
2
)(x+
2
)=0
(x−
2
)=0 or,(x+
2
)=0
x=
2
or x=−
2
Thus ,the zeroes of f(x) are α=
2
and β=−
2
Now,
Sum of the zeroes=α+β=
2
+(−
2
)
=0
and, −(
coefficient of x
2
coefficient of x
)=−(
1
0
)=0
Therefore sum of the zeroes=−(
coefficient of x
2
coefficient of x
)
Product of the zeroes=α×β=
2
×−
2
=−2
and,
coefficient of x
2
constant term
=
1
−2
=−2
Therefore, product of zeros =
coefficient of x
2
constant term
Given :
The polynomial
f(x) =2ˣ² - 5x + 3
Find :
zeroes of the polynomial f(x)= 2x² - 5x + 3
Solution :
By factorizing we have ,
→ 2x² - 5x + 3
→2x² -2x - 3x + 3
→2x(x-1)-3(x-1)
→(2x-3)(x-1)
Now the zeroes are
→ 2x - 3 = 0 and → x - 1 = 0
→ x = 3/2 and → x = 1
Verification of relation
Sum of the zeroes = -b/a
⇒ 3/2 + 1 = -(-5/2)
⇒ (3+2)/2 = 5/2
⇒ 5/2 = 5/2
Product of the zeroes = c/a
⇒ 3/2×1 = 3/2
⇒ 3/2 = 3/2
Verified
I hope it will help you.
Regards.