Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
||
(2 intermediate revisions by the same user not shown) | |||
Line 1: | Line 1: | ||
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i ≠0\; ∀i$. The minimum number of | 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: | + | multiplications needed to evaluate $p$ on an input $x$ is: |
<b>(A) </b>3 | <b>(A) </b>3 | ||
Line 16: | Line 16: | ||
− | As we can see, here we need only | + | As we can see, here we need only three multiplications, so option <b>(A)</b> 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 | + | 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. |
Line 25: | Line 25: | ||
− | + | ||
[[Category: GATE2006]] | [[Category: GATE2006]] | ||
− | [[Category: Mathematics questions]] | + | [[Category: Mathematics questions from GATE]] |
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
We can use just horner's method, according to which, we can write p(x) as :
$$p(x) = a_0 + x(a_1 + x(a_2 + a_3x))$$
As we can see, here we need only three 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.
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
We can use just horner's method, according to which, we can write p(x) as :
$$p(x) = a_0 + x(a_1 + x(a_2 + a_3x))$$
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.