Question

(ii) x2 + 6x -- 8=0 formula method​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² + 6x - 8 = 0.

As we know that,

D = Discriminant Or b² - 4ac.

⇒ α = -b + √b² - 4ac/2a.

⇒ β = -b - √b² - 4ac/2a.

We can also write equation as,

⇒ α = -b + √D/2a.

⇒ β = -b - √D/2a.

⇒ D = (6)² - 4(1)(-8).

⇒ D = 36 + 32.

⇒ D = 68.

Put the value in equation, we get.

⇒ α = -6 + √68/2.

⇒ α = -6 + 2√17/2.

⇒ α = 2(-3 + √17)/2.

⇒ α = -3 + √17.

⇒ β = -6 - √68/2.

⇒ β = -6 - 2√17/2.

⇒ β = 2(-3 - √17)/2.

⇒ β = -3 - √17.

Value of,

⇒ α = -3 + √17.

⇒ β = -3 - √17.

                                                                                                                     

MORE INFORMATION.

Conjugate roots.

If D < 0

One root = α + iβ.

Other root = α - iβ.

If D > 0

One root = α + √β.

Other root = α - √β.