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Question

If x213x+36=0 has p,q as its roots, then which of the following is the equation with the roots p,q ?

A
x2+5x6=0
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B
x25x6=0
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C
x25x+6=0
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D
x2+5x+6=0
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Solution

The correct option is C x25x+6=0

Given that x213x+36=0 has p,q as its roots.
p+q=13
pq=36pq=6
An equation with roots p,q can be written as:
x2(p+q)x+pq=0

So (p+q)2=p+q+2pq
(p+q)2=13+2(6)=13+12=25
p+q=25=5

Therefore the required equation can be written as:
x25x+6=0

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