Suppose a , b denote the distinct real roots of the quadratic polynomial x 2 + 20 x − 2020 and suppose c , d denote the distinct complex roots of the quadratic polynomial x 2 - 20 x + 2020 . Then the value of a c a − c + a d a − d + b c b − c + b d b − d

Step-by-step solution

Finding the sum and product of roots of the two given quadratic equations i.e. a + b = - 20   &   a b = - 2020   . . . . . . . . . . . i c + d = 20   &   c d = 2020   . . . . . . . . . . . i i Now, a c a − c + a d a − d + b c b − c + b d b − d = a 2 c + d − a c 2 + d 2 + b 2 c + d − b c 2 + d 2 = a 2 + b 2 c + d − a + b c 2 + d 2 = a + b 2 − 2 a b c + d − a + b c + d 2 − 2 c d = - 20 2 − 2 - 2020 20 − - 20