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If the sum of the roots of the equation ax+bx+c=0 is equal to the sum of the square of their reciprocals then b²/ac + bc/a²?
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If the sum of the roots of the equation ax+bx+c=0 is equal to the sum ...

Explanation:

Given equation:

The equation given is ax + bx + c = 0, where a, b, and c are constants.
Sum of the roots:

The sum of the roots of the quadratic equation ax^2 + bx + c = 0 is -b/a.
Sum of the square of their reciprocals:

The sum of the square of the reciprocals of the roots is (1/root1)^2 + (1/root2)^2 = (1/root1)^2 + (1/(-b/a - root1))^2.
Equating the sums:

Given that the sum of the roots is equal to the sum of the square of their reciprocals, we have:
-b/a = (1/root1)^2 + (1/(-b/a - root1))^2.
Solving for b²/ac + bc/a²:

We can simplify the above equation to find b²/ac + bc/a².
By solving the equation, we get b²/ac + bc/a² = 1/a².
Therefore, the value of b²/ac + bc/a² is 1/a².
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If the sum of the roots of the equation ax+bx+c=0 is equal to the sum of the square of their reciprocals then b²/ac + bc/a²?
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