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the eq formed by decreasing each of ax 2 +bx+c=0 by 1 is 2x 2 +8x+2=0. then prove b=-c

the eq formed by decreasing each of ax2+bx+c=0 by 1 is 2x2+8x+2=0. then prove b=-c

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:

Hello Student,
Please find answer to your question below

ax^{2} + bx + c = 0
Now if we decrease x by 1, we have
a(x-1)^{2} + b(x-1) + c = 0
a(x^{2}-2x + 1) + b(x-1) + c = 0
ax^{2} + (b-2a)x + (a-b+c) = 0
2x^{2} + 8x + 2 = 0
By comparing,
a = 2
a - b + c = 2
2 - b + c = 2
b = c

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