Question

Condition for quadratic equation to be a perfect square

Answer 1

let the equation be x^2 - bx + c , b and c are integers

now discriminant = b^2 - 4c

let square root of discriminant be Q

so roots are (-b+Q)/2 and (-b-Q)/2

// now watch closely

b^2 - 4c will be even or odd if b is even or odd respectively as 4c is even .

hence Q will be even or odd if b is even or odd respectively


in both of those cases -b + Q and - b - Q are divisible by 2

so roots will be integers .

// Hope it helps
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