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Function $h(x)$ is defined as $x^3-3 x^2-b x+25 \cdot(x-2)$ is one fac
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12 Apr 2025, 00:57
12 Apr 2025, 00:57
Expert Reply
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Question Stats:
33% (02:05) correct
66% (02:11) wrong based on 3 sessions
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Function $\(h(x)\)$ is defined as $\(x^3-3 x^2-b x+25 \cdot(x-2)\)$ is one factor of $\(h(x)-1\)$. For what values of $\(x\)$ will $\(h(x)\)$ be equal to 1 ? (Indicate all the possible answers)
(A) -4
(B) -3
(C) -2
(D) 0
(E) 3
(F) 4
(A) -4
(B) -3
(C) -2
(D) 0
(E) 3
(F) 4
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Re: Function $h(x)$ is defined as $x^3-3 x^2-b x+25 \cdot(x-2)$ is one fac
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16 Apr 2025, 04:00
16 Apr 2025, 04:00
Expert Reply
$\(h(x)-1=x^3-3 x^2-b x+24\)$ and $\(x-2\)$ is factor of $\(h(x)-1\)$.
From this, we get $\(b=10\)$.
Substituting the value of $\(B\)$ in the given equation, the equation becomes $\(h(x)-1=x^3-3 x^2-10 x+24\)$. Only $\(B\)$ and $\(F\)$ satisfy the equation. Thus, the correct options are $\(B\)$ and $\(F\)$.
From this, we get $\(b=10\)$.
Substituting the value of $\(B\)$ in the given equation, the equation becomes $\(h(x)-1=x^3-3 x^2-10 x+24\)$. Only $\(B\)$ and $\(F\)$ satisfy the equation. Thus, the correct options are $\(B\)$ and $\(F\)$.
gmatclubot
Re: Function $h(x)$ is defined as $x^3-3 x^2-b x+25 \cdot(x-2)$ is one fac [#permalink]
16 Apr 2025, 04:00
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