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if (ax+b)(ax+c)=4x^2-25 for all values of x, and a, b, and c are constants, what is the value of b+c?

User Nikketa
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1 Answer

3 votes

Answer: 10.

Explanation:

You are given the equation

(ax+b)(ax+c)=4x^2-25

Expand the Left hand side by opening the bracket.

a^2x^2 + axc + abx + bc

a^2x^2 + (axc + abx) + bc = 4x^2 + 0x - 25

From the equation above, we can see that;

a^2x^2 = 4x^2

a^2 = 4

a = √4

a = 2

Also, axc + abx = 0x

axc = abx

ax will cancel out from both sides

c = b

From the equation, bc = 25

But c = b. Substitute c for b

b^2 = 25

b = √25

b = 5 = c

b + c is therefore 5 + 5 = 10

User JLK
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