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Q.

Suppose a, b denote the distinct real roots of the quadratic polynomial x2+20x2020
And suppose c, d denote the distinct complex roots of the quadratic polynomial x220x+2020.
Then the value of ac(ac)+ad(ad)+bc(bc)+bd(bd)=
 

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a

8080

b

16000

c

8000

d

0

answer is C.

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Detailed Solution

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a+b=20 and ab=2020.1c+d=20 and cd=2020           .2
Now, ac(ac)+ad(ad)+bc(bc)+bd(bd)
=a2(c+d)ac2+d2+b2(c+d)bc2+d2=a2+b2(c+d)(a+b)c2+d2=(a+b)22ab(c+d)(a+b)(c+d)22cd=(20)22(2020)(20)(20)(20)22(2020)
= 16000

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