Question

α,β are roots of y²-2y-7=0 find, a²+β³

Answer 1

a+b=2 and ab=-7 from given equation.
a²+b²=(a+b)²-2ab
=2²-2(-7)
=4+14
= 18. ans..
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Answer 2

Answer:

∝² + β² = 18

Step-by-step explanation:

The given equation is y² - 2y - 7 = 0.

Here, a = 1, b = - 2, c = - 7.

∝ + β = - b / a

⇒ ∝ + β = - ( -2 ) / 1

⇒ ∝ + β = 2 ..... (1)

∝.β = c / a

⇒ ∝.β = - 7 / 1

⇒ ∝.β = - 7 .......(2)

Now,

∝² + β² = (∝ + β)² - 2∝β

⇒ ∝² + β² = ( 2 )² - 2 ( - 7 ) ... [From (1) and (2)]

⇒ ∝² + β² = 4 + 14

∴ ∝² + β² = 18