in Numerical Methods
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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:

  1. 3
  2. 4
  3. 6
  4. 9
in Numerical Methods
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4 Comments

we can factorize the equation (x+r1)(x+r2)(x+r3), where r1,r2 and r3 are root of equation
so 3 multiplication
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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 ?
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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 .

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3 Answers

29 votes
29 votes
Best answer
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.
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2 Comments

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

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@sourav I agree, it should be 6.
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5 votes
5 votes
a_0+x(a_1+x(a_2+a_3x)) so 3 multiplications required
5 votes
5 votes

Answer will be 3

mul= pair of brackets

p(x)=a0+x(a1+x(a2+a3(x)))

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2 Comments

3 or 6 ?
2
2
3 multiplications
1
1
Answer:

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