Question

Which polynomial function has a leading coefficient of 1 and roots /7 and - /3 with multiplicity 1?

0 px)=(x-7)(x+ v)
o Rx)= (x + √2)(x-√3)
9-(x-»2)(x-7)(x-v3)(x-V3)
O Rx)=(x-„3)(** 3)(x-5) (x+ v)

Answer 1

• A. f(x) = (x - √2)(x + √3)

Explanation:

Leading coefficient is 1, multiplicity is 1, roots are √2 and -√3. It means the function is the product of two binomials.

The function with the roots of a and b is:

• f(x) = (x - a)(x - b)

Substitute and and b:

• f(x) = (x - √2)(x - (-√3)) ⇒
• f(x) = (x - √2)(x + √3)

Correct choice is A

Answer 2

for a

f(x)=(x-√2)(x+√3)

f(x)=(x-√2)(x-(-√3))

it has coefficient of 1 and roots √2 and -√3 with multiplicity 1

for second

f(x)= (x + √2)(x-√3)

f(x)= (x -( √2))(x-√3)

it has coefficient of 1 and but not roots √2 and -√3 with multiplicity 1

for third

f(x)=(x-√2)(x-√2)(x-√3)(x-√3)

f(x)=(x-√2)²(x-√3)²

it has coefficient of 1 and but not roots √2 and -√3 with multiplicity 1

for forth

f(x)=(x-√2)(x+√2)(x-√3)(x+√3)

f(x)=(x²-2)(x²-3)it has coefficient of 1 and but not roots √2 and -√3 with multiplicity 1

So

f(x)=(x-√2)(x-(-√3)) is a required answer.