Question

If α and β are the zeroes of x2−5x+4 then find
a)α+β
b)αβ
c)α
2
+β2

d) α
2
β + αβ​

Answer 1

Answer:

a ) 5

b ) 4

c ) 17

d ) 20

Step-by-step explanation:

x² - 5x + 4 = 0

x² - x - 4x + 4 = 0

x ( x - 1 ) - 4 ( x - 1 ) = 0

( x - 1 ) ( x - 4 ) = 0

x - 1 = 0

x = 1

x - 4 = 0

x = 4

The zeroes are 4 and 1.

Let,

α = 4

β = 1

a )

α + β

= 4 + 1

= 5

b )

αβ

= 4 × 1

= 4

c )

α² + β²

= 4² + 1²

= 16 + 1

= 17

d )

α²β + αβ

= 4² ( 1 ) + 4

= 4² + 4

= 16 + 4

= 20