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If b, c, and h are constants such that x2 + bx + c = (x + h)2, what is
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26 Oct 2021, 01:36
26 Oct 2021, 01:36
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If b, c, and h are constants such that \(x^2 + bx + c = (x + h)^2\), what is the value of c if b = 10?
See more on these concepts our GRE Quant Book and the GRE Math Essentials project
Show: ::
25
See more on these concepts our GRE Quant Book and the GRE Math Essentials project
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Re: If b, c, and h are constants such that x2 + bx + c = (x + h)2, what is
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26 Oct 2021, 05:59
26 Oct 2021, 05:59
1
Carcass wrote:
If b, c, and h are constants such that \(x^2 + bx + c = (x + h)^2\), what is the value of c if b = 10?
See more on these concepts our GRE Quant Book and the GRE Math Essentials project
Show: ::
25
See more on these concepts our GRE Quant Book and the GRE Math Essentials project
Given: \(x^2 + bx + c = (x + h)^2\)
Expand the right side to get: \(x^2 + bx + c = x^2 + 2hx + h^2\)
Substitute \(b = 10\) to get: \(x^2 + 10x + c = x^2 + 2hx + h^2\)
When we compare the two equations we can see that \(10 = 2h\), which we can solve to get \(h = 5\)
Substitute \(h = 5\) to get: \(x^2 + 10x + c = x^2 + 2(5)x + 5^2\)
Evaluate to get: \(x^2 + 10x + c = x^2 + 10x + 25\)
At this point it's clear that \(x = 25\)
Answer: \(25\)
Re: If b, c, and h are constants such that x2 + bx + c = (x + h)2, what is
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30 Sep 2024, 17:17
30 Sep 2024, 17:17
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