Question

the number of polynomials have zeros 2 and 1 is
​

Answer 1

only one polynomial

this is your answer

Answer 2

Answer:

The number of polynomial have zeroes 2 and 1 can be infinite

Step-by-step explanation:

Let the required Quadratic polynomial be f (x) = ax² + bx + c

We know for the given equation f (x) = ax² + bx + c,

Sum of zeroes = -b/a

According to question,

The zeroes of polynomial are 2 and 1

Substituting the values,

2 + 1 = -b/a

3 = -b/a

3 / 1 = -b/a

On comparing we get,

b = -3 and a = 1

Also we know,

Product of zeroes = c/a

Substituting the values,

2 * 1 = c/a

2 = c/a

2 = c

Substituting values of a, b and c we get,

f ( x ) = 1 ( x² ) - 3 ( x ) + 2

So, The equation is f(x) =  x² - 3x + 2

[ Also, We know that zeroes does not change if the polynomial is divided or multiplied by constant]

Let the constant be ' k '

Multiplying the equation with ' k '

f (x) = kx² - 3kx + 2k   [ Where k is real number}

Dividing the equation by ' k '

f (x) = ( x² / k ) - ( 3/k ) x + ( 2/k )  [ Also, k is a non-zero real number]

Therefore, there are infinitely many polynomials

Hence,

The number of polynomial have zeroes 2 and 1 can be infinite.