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Question

If one root of the quadratic equation ax2+bx+c=0 is 3−4i, then 31a+b+c is equal to

A
0
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B
2a
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C
2b
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D
2c
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Solution

The correct option is D 2c
Since one of the root of the quadratic equation ax2+bx+c=0 is 34i, therefore, it is obvious that 3+4i is also the root of the given equation. Now, consider

Sum of zeroes
(34i)+(3+4i)=ba6=bab=6a....(1)
Product of zeroes
(34i)(3+4i)=ca32(4i)2=ca(x2y2=(x+y)(xy))916i2=ca9+16=ca(i2=1)25=cac=25a....(2)

Now consider 31a+b+c as shown below:

31a+b+c=31a6a+25a(Fromeqns1and2)=50a=2×25a(Fromeqn2)=2c

Hence, 31a+b+c=2c.

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