Question

Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x + 4)(x – i)(x – 2) f(x) = (x – 3)(x + 4)(x – i)(x – 2) f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2) f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

Answer 1

Answer:

(1). f(x) = 3(x + 4)(x - i)(x - 2)

Step-by-step explanation:

If f(x) = 3(x + 4)(x - i)(x - 2) = 0, then zeroes of f(x) are

x + 4 = 0 ⇒ $x_{1}$ = - 4

x - i = 0 ⇒ $x_{2}$ = i

x - 2 = 0 ⇒ $x_{3}$ = 2

Terms with greatest exponent is 3x³ ⇒ leading coefficient is 3

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which polynomial function has a leading coefficient of 3 and roots - 4 , i , and 2 , all with multiplicity 1

• f(x) = 3(x + 4)(x – i)(x – 2)

• f(x) = (x – 3)(x + 4)(x – i)(x – 2)

• f(x) = (x – 3)(x + 4)(x – i)(x + i)(x – 2)

• f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

EVALUATION

Here we have to find the the polynomial function has a leading coefficient of 3 and roots - 4 , i , and 2 , all with multiplicity 1

We know that complex roots occur in pair

Since it is given that one root is i

So another root must be - i

Thus the polynomial function has four roots - 4 , i , - i , 2

Now leading coefficient is 3 and each root with multiplicity 1

Hence the required polynomial function is

f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

FINAL ANSWER

Hence the correct option is

f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If p(x) = 2x2 + 4x + 6 is a quadratic polynomial then what is the value of sum of zeroes?

https://brainly.in/question/31024345

2. write a quadratic polynomial sum of whose zeroes is 2 and product is -8

https://brainly.in/question/25501039