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Question

The coefficient of x in the equation ax2+bx+c=0 was wrongly taken as 17 instead of 30 and its roots came out to be -2, -15. The actual roots were:

A
-2,-15
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B
-3,-10
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C
-5,-6
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D
None of these
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Solution

The correct option is D None of these
The sum of the roots = -b/a
The product of the roots = c/ a
If we know the sum and the product of the roots, the quadratic equation is x2(b/a)x+(c/a)=0
In the both cases, the product of roots is same (i.e. product of the roots c=(15)×(2)=30)
So, the wrong equation = x2+17x+30=0
The actual equation = x2+30x+30=0
Roots of a quadratic equation x=b±b24ac2a
By using the above equation, actual roots = x=30±3024×302
x=30±7802
x=15±195

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