30 votes 30 votes Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is: 3 4 6 9 Numerical Methods gatecse-2006 numerical-methods normal isro2009 + – gatecse asked Sep 15, 2014 gatecse 11.3k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments reena_kandari commented Aug 11, 2017 reply Follow Share we can factorize the equation (x+r1)(x+r2)(x+r3), where r1,r2 and r3 are root of equation so 3 multiplication 0 votes 0 votes Rupendra Choudhary commented Dec 25, 2017 reply Follow Share Hello reena Doesn't (x+r1)(x+r2)(x+r3) need 2 multiplication ? Why're you sure enough that coefficient of $x^{3}$ in our general given equation would be 1 ? 0 votes 0 votes Vijay Dulam commented Aug 20, 2018 reply Follow Share apply the Horner's Rules P(x)= a0 + a1x + a2x^2 + a3x^3 P(x)= a0 +(( a1+a2x + a3x^2) x ) // 1 multipication taking the x common P(x)= a0 +(( a1+(a2 + a3x ) x ) x // 2 multipication in x in inner bracket P(x)= a0 +( ( a1+(a2 + a3x ) x ) x ) // 3 multipication entire bracket Minimum 3 Multipication required . 1 votes 1 votes Please log in or register to add a comment.
Best answer 29 votes 29 votes 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. gatecse answered Sep 15, 2014 selected Jun 20, 2016 by Desert_Warrior gatecse comment Share Follow See all 2 Comments See all 2 2 Comments reply sourav. commented Mar 6, 2018 reply Follow Share Sir, if the question would be-: Total number of arithmetic operation required,then answer would be $6(3+3)$.right? https://gateoverflow.in/2045/gate2014-3-11 0 votes 0 votes Akhilesh Singla commented Apr 19, 2018 reply Follow Share @sourav I agree, it should be 6. 1 votes 1 votes Please log in or register to add a comment.
5 votes 5 votes a_0+x(a_1+x(a_2+a_3x)) so 3 multiplications required Bhagirathi answered Sep 19, 2014 Bhagirathi comment Share Follow See all 0 reply Please log in or register to add a comment.
5 votes 5 votes Answer will be 3 mul= pair of brackets p(x)=a0+x(a1+x(a2+a3(x))) srestha answered Nov 24, 2015 edited Nov 24, 2015 by srestha srestha comment Share Follow See all 2 Comments See all 2 2 Comments reply Umang Raman commented Nov 24, 2015 reply Follow Share 3 or 6 ? 2 votes 2 votes tiger commented Nov 24, 2015 reply Follow Share 3 multiplications 1 votes 1 votes Please log in or register to add a comment.