(ii) x2 + 6x -- 8=0 formula method
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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.
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