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Note that in question paper, $a_3x^2$ is written instead of $a_3x^3$, but for $a_3x^2$, answer is 2, because we can save  
 
Note that in question paper, $a_3x^2$ is written instead of $a_3x^3$, but for $a_3x^2$, answer is 2, because we can save  
 
one more multiplication between $a_3$ and x, but 2 is not in the options, so I guess question paper had a printing mistake.
 
one more multiplication between $a_3$ and x, but 2 is not in the options, so I guess question paper had a printing mistake.
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[[Category: Mathematics]]
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[[Category: GATE2006]]
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[[Category: Previous year GATE questions]]

Revision as of 13:52, 14 April 2014

Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i ≠0\; ∀i$. The minimum number of multiplications needed to evaluate p on an input x is:

(A) 3

(B) 4

(C) 6

(D) 9

Solution by Happy Mittal

We can use just horner's method, according to which, we can write p(x) as : $$p(x) = a_0 + x(a_1 + x(a_2 + a_3x))$$ So as we can see, here we need only 3 multiplications, so option (A) is correct.

Note that in question paper, $a_3x^2$ is written instead of $a_3x^3$, but for $a_3x^2$, answer is 2, because we can save one more multiplication between $a_3$ and x, but 2 is not in the options, so I guess question paper had a printing mistake.


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Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i ≠0\; ∀i$. The minimum number of multiplications needed to evaluate p on an input x is:

(A) 3

(B) 4

(C) 6

(D) 9

Solution by Happy Mittal[edit]

We can use just horner's method, according to which, we can write p(x) as : $$p(x) = a_0 + x(a_1 + x(a_2 + a_3x))$$ So as we can see, here we need only 3 multiplications, so option (A) is correct.

Note that in question paper, $a_3x^2$ is written instead of $a_3x^3$, but for $a_3x^2$, answer is 2, because we can save one more multiplication between $a_3$ and x, but 2 is not in the options, so I guess question paper had a printing mistake.