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Question

If A.M. and H.M. of the roots of a quadratic equation are 8 and 5 respectively, then the equation is

A
x2+16x40=0
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B
x216x40=0
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C
x2+16x+40=0
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D
x216x+40=0
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Solution

The correct option is D x216x+40=0
Let the required roots be a and b
Now,
a+b2=8a+b=16(1)
2aba+b=5
Using equation (1),
2ab16=5ab=40(2)

Now,
Sum of roots =16,
Product of roots =40
Hence, the required quadratic equation is
x216x+40=0

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