Question

The roots of the equation ax2 + bx + c = 0 will be reciprocal if:

Answer 1

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Let k be one of the root of the given equation.

According to the problem,

1/k will be the other root of the given equation.

We know that, product of the roots of the equation = c/a.

Therefore, k × 1/k = c/a.

or, 1 = c/a.

or, a = c [multiplying a on both sides].

The roots of the equation ax2 + bx + c = 0 will be reciprocal if a = c.

Therefore, a = c or c = a.


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Answer 2

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The roots of the equation ax2 + bx + c = 0 will be reciprocal if:when c=a

ax^2 + bx + c = 0 

the roots are: 

x = [- b ± √(b^2 - 4ac)]/2a 

to be reciprocals, 

[- b + √(b^2 - 4ac)]'/2a = 2a/[- b - √(b^2 - 4ac)] 

solve...cross multiply to get... 

b^2 - (b^2 - 4ac) = 4a^2 

4ac = 4a^2 

c = a 


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