The sum of the squares of the root is 4113
In a quadratic equation ax² + bx + c , the sum of the roots is -b/a and the product of the roots is c/a
Let m, n be roots of the given equation.
So,
m - n = 75 -1)
m + n = 51 (as sum of roots of a quadratic equation is -b/a) -2)
adding both equations 1) and 2)
2m = 75 + 51
2m = 126
m = 63
substituting value of m in equation 1 we get
63 - n = 75
n = -12
So the sum of squares of the roots of the equation is = 63² + -12²
= 3969 + 144
= 4113
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