Question

If αand β are the zeros of the polynomial 2x ²–7x + 3. alpha/beta+beta/alpha

Answer 1

Answer:

27/8

Step-by-step explanation:

here the given polynomial is p (x) = 2x² - 7x + 3

find out the roots by splitting the middle term

→ 2x² - 7x + 3 = 0

→ 2x² - 6x - x + 3 = 0

→ 2x ( x - 3 ) - 1 ( x - 3 ) = 0

→ ( 2x - 1 ) ( x - 3 ) = 0

→ x = 1/ 2 OR x = 3

▶here the roots are α and β

therefor, α = 1/2 OR β = 3

α³ x β³ = ( 1/2 )³ x ( 3 )³

= ( 1 / 8 ) x ( 27 )

=27/8

Answer 2

Answer:

α,β are the zeroes of the polynomial

p(x)=2x ²–7x + 3.

Sum of zeroes (α+β) = -b/a = -(-7)/2 = 7/2

Product of zeroes αβ= c/a = 3/2

α/β + β/α = α² + β² / αβ

∴ (a² + b²) = (a+b) ² - 2ab / αβ

= (α+β) ² - 2αβ/ αβ

= (7/2) ² - 2 (3/2)

____________

(3/2)

= -19/14