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Question

Two numbers whose sum is 6 and the absolute value of whose difference is 8 are the roots of the equation:

A
a26a+7=0
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B
a26a7=0
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C
a26a8=0
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D
a26a+8=0
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Solution

The correct option is C a26a7=0
Let roots of equation be p and q
Equation is a2(p+q)a+pq=0

Given that,
p+q=6....(1)
|pq|=8....(2)

Squaring and adding both the equations, we get
2(p2+q2)=100
p2+q2=50

Squaring equation (1), we get
p2+q2+2pq=36
pq=7

Equation is a26a7=0

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