2. Find the quadratic polynomical whose
zeroes are
are - 2 and -5 . verify the
relationship blw The zeroes &
coefficients.
Answers
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Step-by-step explanation:
Let f(x)=px
2
+(2q−p
2
)x−2pq
f(x)=px
2
+2qx−p
2
x−2pq
=x(px+2q)−p(px+2q)
=(x−p)(px+2q)
On putting f(x)=0, we get (x−p)(px+2q)=0
⇒x−p=0 or px+2q=0
⇒x=p or x=
p
−2q
Thus, the zeroes of the given polynomial px
2
+(2q−p
2
)x− 2pq are p and
p
−2q
Verification:
Sum of zeroes =α+β=p+
p
(−2q)
=
p
p
2
−2q
or
=−
Coefficient of x
2
Coefficient of x
Product of zeroes
=−
p
(−p
2
+2q)
=
p
p
2
−2q
=αβ=p×
p
−2q
=−2q
=
Coefficient of x
2
Constant term
=
p
−2pq
=−2q
So, the relationship between the zeroes and the coefficients is verified.
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