Question

From a quadratic polynomial whose zeroes are 3-√3/5 and 3+√3/5

Answer 1

$\boxed{\textbf{\large{Step-by-step explanation:}}}$

◼here we have given the two zeros of the quadratic polynomial

let us suppose,

α = 3-√3/5

β = 3+√3/5

◾for making a quadratic equation, we know the equation to make a quadratic polynomial , ( if α and β are the two roots of quadratic equation)

x² - (α + β )x + ( α x β )

therefor , Now find the values of

( α + β ) and ( α x β )

( α + β ) = 3 - √3/5 + 3 + √3/5

∴ (α + β ) = 6

( α x β ) = ( 3 - √3 / 5 ) ( 3 + √3 /5 )

we know , the identity

a² - b² = ( a + b) ( a - b) , from that

= (3 )² - (√3 / 5 )²

= 9 - (3 / 25 )

= (225 - 3 ) / 25

= 222/ 25

∴ ( α x β ) = 8.88

substitute the values of ( α + β ) and ( α x β )

x² - (α + β )x + ( α x β )

x² - ( 6 )x +( 8.88 )

◼Therefor, The final equation is whose zeroes are 3-√3/5 and 3+√3/5

x² - 6x +8.88