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Question

Find the values of p and q for which x=34 and x=−2 are the roots of the equation px2+qx−6=0

A
p=4,q=5
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B
p=4,q=5
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C
p=4,q=5
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D
p=4,q=5
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Solution

The correct option is B p=4,q=5
The quadratic equation is px2+qx6=0 ......(i)
Given, x=34 and x=2 are the roots of the quadratic equation.
Thus, putting x=34 in equation (i) we get,
p(34)2+q×346=0
p×916+3q46=0
9p+12q9616=0
9p+12q96=0
3p+4q32=0 ....(ii)
Now, putting x=2 in equation (i), we get
p(2)2+q(2)6=0
4p2q6=0
2pq3=0 ....(iii)
Now, multiplying equation (iii) by 4, we get
8p4q12=0 ....(iv)
Now, adding (ii) and (iv), we get
11p44=0
p=4411
p=4
Now, putting the value of p in equation (iii), we get
2pq3=0
2×4q3=0
8q3=0
q=38
q=5
q=5

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