Suppose a, b denote the distinct real roots of the quadratic polynomial x^2 +20x−2020 and suppose c, d denote the distinct complex roots of the…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (D) 16000. Finding the sum and product of roots of the two given quadratic equations i.e. a+b=-20 & ab=-2020 ...........i c+d=20 & cd=2020 ...........ii Now, aca−c+ada−d+bcb−c+bdb−d =a^2c+d−ac^2+d^2+b^2c+d−bc^2+d^2 =a^2+b^2c+d−a+bc^2+d^2 =a+b^2−2abc+d−a+bc+d^2−2cd =-20^2−2-202020−-2020^2−22020 (using equations i & ii) =16000

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 $a c (a - c) + a d (a - d) + b c (b - c) + b d (b - d)$

Solution

Relevant Questions

Suppose a, b denote the distinct real roots of the quadratic polynomial x 2 +20x−2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2-20x+2020. Then the value of aca−c+ada−d+bcb−c+bdb−d

Solution

Relevant Questions

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 $a c (a - c) + a d (a - d) + b c (b - c) + b d (b - d)$