Question

Hey mate, please solve this quadratic equation....☆○●□■The best answer will be selected as brainliest...♤♡◇♧​

Answer 1

Answer:

Option(C)

Step-by-step explanation:

Given Equation is x² - x - 1 = 0

On comparing with ax² + bx + c = 0, we get

a = 1, b = -1, c = -1.

α,β are the roots of the quadratic equation.

(i) Sum of roots:

⇒ α + β = -b/a

⇒ α + β = 1

(ii) Product of roots:

⇒ αβ = c/a

⇒ αβ = -1

Now,

α² + β² = (α + β)² - 2αβ

            = (1)² - 2(-1)

            = 3.

α³ + β³

= (α + β)(α² + β² - αβ)

= (1)(3 + 1)

= 4

∴ α³ + β³ = 4

Hope it helps!

Answer 2

We are given the equation  

x^2 = x + 1

=> x^2 - x - 1 = 0

As it is given that the roots of this equation are α, β, we can, by the use of the sum and product of roots formulae, say that,

α + β = -(-1)/1 = 1

αβ = -1

Now, we are asked to find the value of

α^2/β - β^2/α.

= (α^3 - β^3) / αβ

= (α - β)(α^2 + αβ + β^2) / -1

= -√[(α + β)^2 - 4αβ] [(α + β)^2 - αβ]

= -√[1 - 4(-1)] (1 - (-1))

= -2√5