Question

ans this.......... class 10​

Answer 1

Answer:

α/β + β/α  = (p² - 2q)/q

Step-by-step explanation:

polynomial x² - px + q = 0 whose zeroes are α and β

∴ α/β + β/α

= (α² + β²)/αβ                 --- (1).

sum of the zeroes of the polynomial  x² - px + q = 0

α + β = -(-p)/1 = p

α + β = p                    ---(2).

products of the zeroes of the polynomial x² - px + q = 0

αβ = q/1 = q

αβ = q             --(3).

∴ (α + β)² = α² + β² + 2αβ

α² + β² = (α + β)² - 2αβ

put the value of eq. 2 and 3

we get ,

α² + β² = p² - 2q        --(4)

put the value of eq. 3 and 4 in eq. 1

(α² + β²)/αβ  

( p² - 2q)/q

threfore ,  α/β + β/α = (p² - 2q)/q

Answer 2

Step-by-step explanation:

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