Question

find the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively 2/3,5

Answer 1

Answer:

x^2 - ( 2 / 3 )x + 5

Step-by-step explanation:

We know,

            Quadratic polynomials are written in the form of x^2 - Sx + P represent S as the sum of roots and P as the product of roots.

Therefore,

 let that polynomial be quadratic to x.

So,

  Polynomial is :

⇒ x^2 - ( 2 / 3 )x + 15

⇒ ( 3x^2 - 2x + 15 ) / 3

⇒ ( 1 / 3 )( 3x^2 - 2x + 15 )

 or we can directly say 3x^2 - 2x + 15  or  x^2 - ( 2 / 3 )x + 5

Answer 2

⠀⠀ || ✪ ϙᴜᴇsᴛɪᴏɴ ✪ ||

find the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively 2/3 , 5

⠀⠀ || ✪.ANSWER.✪ ||

Let,

• First zero = α
• Second zero = β

GIVEN:-

• α + β = 2/3
• α.β = 5

FIND:-

• Quadratic polynomial

EXPLANATION:-

we know,

Equation of polynomial ,

[ x² - (α + β)x - α.β ] = 0

Keep above values,.

➩ x² - (2/3)x + 5 = 0

➩ 3x² - 2x + 15 = 0

THUS:-

Required equation will be,

• 3x² - 2x + 15 = 0

|| ✪.Verification.✪ ||

we know,

★ Sum of zeroes = [ -(coefficient of x)/(coefficient of x²)]

➩ (α + β ) = -(-2)/3

➩ (α + β ) = 2/3

Again,

★ product of zeroes = [ (constant part)/(coefficient of x²)]

➩ (α.β ) = 15/3

➩ (α.β ) = 5

That's proved .