Question

if the roots of 2016x²+bx+c =0 are 5/63,-7/32,then b+6c is equal to __________

find it out with proper step!

Answer 1

The roots of the equation satisfies the equation :

p(x) = 2016x²+bx+c = 0

p(5/63)
0 = 2016(5/63)² + b(5/63) + c
50400/3969 + (5/63)b + c = 0
-(5600/441) = (5b+63c)/63
5b+63c = -800
b = (-800-63c)/5

p(-7/32)
= 2016(-7/32)² + b(-7/32) + c = 0
98784/1024 = c - (7/32)b
32c-7b = 3087
b = (32c-3087)/7

-(800+63c)/5 = (32c-3087)/7
-5600 + 441c = 160c - 15435
281c = -9835
c = -35

b = -[800+63(-35)]/5
b = 281
________________________
Now,

b+6c
= 281 + 6(-35)
= 281-210
= 71
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