Question

if x and B are the zeros of a polynomial such that X + Y is equal to 5 x b is equal to 4 then write the polynomial​

Answer 1

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Sum of zeroes is = 5

• Product of zeroes is = 4

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the polynomial?

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let α and β are the zeroes of required polynomial.

Given that,

Sum of zeroes is = 5

Product of zeroes is = 4

Therefore,

α + β = 5

αβ = 4

Formula for a quadratic polynomial is given

x² - (α + β)x + αβ

Now put the given values

f(x) = x² - (α + β)x + αβ

= x² -(5)x + 4

=x² - 5x +4 = 0

Hence, the required polynomial is

⠀⠀⠀⠀=⠀x² - 5x +4 = 0

Answer 2

Answer:

x^2-5x+4

Explanation:

given:-

           • Sum of zeroes is = 5

• Product of zeroes is = 4

• What's the polynomial?

Let α and β are the zeroes of required polynomial.

Given that,

Sum of zeroes is = 5

Product of zeroes is = 4

Therefore,

α + β = 5

αβ = 4

Formula for a quadratic polynomial is given

x² - (α + β)x + αβ

Now put the given values

f(x) = x² - (α + β)x + αβ

= x² -(5)x + 4

=x² - 5x +4 = 0

Hence, the required polynomial is

⠀⠀⠀⠀=⠀x² - 5x +4 = 0