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The roots of the equation ax^2 + bx + c = 0 have to be changed from x1, x2 to 2*x1 and 2*x2 respectively. The change in a and b required for this has to be estimated.
ax^2 + bx + c = 0
=> (x - x1)(x - x2) = 0
=> x^2 - (x1 + x2)*x + x1*x2 = 0 ...(1)
As this has to be in the form ax^2 + bx + c = 0
When the roots become 2*x1 and 2*x2
(x - 2*x1)(x - 2*x2) = 0
=> x^2 - (2*x1 + 2*x2) + 4*x1*x2 = 0
=> x^2 - 2*(x1 + x2) - 4*x1*x2 = 0 ...(2)
Comparing (1) and (2) it is seen that b becomes twice and c becomes 4 times.
The change in ax^2 + bx + c = 0 for the roots to become double are b becomes twice and c becomes 4 times their original value.
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