Find a relation between p and q if one zero of x2 +pc+q is 37 than the other
Answers
Answer:
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Step-by-step explanation:
ANSWER
We know that if m and n are the roots of a quadratic equation ax
2
+bx+c=0, the sum of the roots is m+n=−
a
b
and the product of the roots is mn=
a
c
.
Let m and n be the roots of the given quadratic equation x
2
+px+q=0. It is given that one of the root is three times the other, therefore,
m=3n........(1)
The equation x
2
+px+q=0 is in the form ax
2
+bx+c=0 where a=1,b=p and c=q.
Using equation 1, the sum of the roots is:
m+n=−
a
b
=−
1
p
=−p
⇒m+n=−p
⇒3n+n=−p
⇒4n=−p
⇒n=−
4
p
....(2)
Using equation 1, the product of the roots is
a
c
that is:
mn=
a
c
=
1
q
=q
⇒n=−p
⇒(3n×n)=q
⇒3n
2
=q......(3)
Now, substitute equation 2 in equation 3 as follows:
(3n×n)=q
⇒3(−
4
p
)
2
=q
⇒(3×
16
p
2
)=q
⇒
16
3p
2
=q
⇒3p
2
=16q
Hence, the value of 3p
2
=16q.