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# If f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, what is the value of a +

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If f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, what is the value of a +  [#permalink]

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27 Nov 2019, 02:05
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If $$f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f$$, what is the value of $$a + b + c + d + e + f$$?

(1) The graphs of $$y=5$$, $$y=3x+2$$, and $$y=f(x)$$ all intersect at the same point on the xy-coordinate plane.

(2) $$(a+b)(c+d)(e+f)=0$$

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Re: If f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, what is the value of a +  [#permalink]

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27 Nov 2019, 04:12
Bunuel wrote:
If $$f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f$$, what is the value of $$a + b + c + d + e + f$$?

(1) The graphs of $$y=5$$, $$y=3x+2$$, and $$y=f(x)$$ all intersect at the same point on the xy-coordinate plane.

(2) $$(a+b)(c+d)(e+f)=0$$

$$f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f$$
$$f(1) = a1^5 + b1^4 + c1^3 + d1^2 + e1 + f = a + b + c + d + e + f$$
--> We have to find the value of f(1).

(1) The graphs of $$y=5$$, $$y=3x+2$$, and $$y=f(x)$$ all intersect at the same point on the xy-coordinate plane.
Point of intersection of $$y=5$$, $$y=3x+2$$ is
--> $$5 = 3x + 2$$
--> $$3 = 3x$$
--> $$x = 1$$
Point of intersection = $$(x, y) = (x, f(x)) = (1, 5)$$
--> When $$x = 1 & f(1) = 5$$

We Know, $$f(1) = a + b + c + d + e + f$$
--> $$a + b + c + d + e + f = 5$$ --> Sufficient

(2) $$(a+b)(c+d)(e+f)=0$$
--> Either $$a + b = 0$$ ....... (1) or $$c + d = 0$$ ....... (2) or $$e + f = 0$$ ....... (3)
Nothing can be said about the value of $$a + b + c + d + e + f$$ as we do not whether (1) or (2) or (3) alone is true or all of them are true --> Insufficient

IMO Option A
Re: If f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, what is the value of a +   [#permalink] 27 Nov 2019, 04:12
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