If the difference of roots of the equation \( \Large x^{2}-bx+c=0 \) be 1, then;

A) \( \Large b^{2}-4c-1=0 \)
B) \( \Large b^{2}-4c=0 \)

C) \( \Large b^{2}-4c+1=0 \)
D) \( \Large b^{2}+4c-1=0 \)

Correct answer:
A) \( \Large b^{2}-4c-1=0 \)

Description for Correct answer:
Let \( \Large \alpha \) and \( \Large \beta \) are the roots of equation \( \Large x^{2}-bx+c=0 \)

=> \( \Large \alpha + \beta = b\ and\ \alpha \beta = c\)

=> \( \Large \alpha + \beta = \sqrt{ \left( \alpha + \beta \right)^{2}-4 \alpha \beta } \)

=> \( \Large 1 = \sqrt{b^{2}- 4c} \)

=> \( \Large b^{2}-4c-1=0 \)

Please provide the error details in above question

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