Question

if α and β are the zeroes of the quadratic polynomial f(x)= x^2-4x+3, find the value of α^4β^2+α^2β^4.

​

Answer 1

Answer:

90

Step-by-step explanation:

Polynomials written in form of x^2 - Sx + P, represent S as sum of roots and P as product of roots.

Here, if a and b are roots-

Sum = a + b = 4

Product = ab = 3

We are said to find-

= > a⁴b² + a²b⁴

= > a²b²( a² + b² )

= > (ab)²( a² + b² )

= > product² ( a² + b² )

= > 3² ( a² + b² )

= > 9( a² + b² )

a² + b² = ( a + b )² - 2ab

= > 9[ ( a + b )² - 2ab ]

= > 9[ sum² - 2product ]

= > 9[ 4² - 2(3)]

= > 9( 16 - 6 ) = 90