Question

by quadratic equation ​

Answer 1

Question:

Solve the given quadratic equation:

x² + x + 1 = 0

Answer:

The roots of the given quadratic equation are

$\displaystyle{\boxed{\red{\sf\:x\:=\:\dfrac{-\:1\:+\:\sqrt{-\:3}}{2}}}\sf\:\:\:OR\:\:\:\boxed{\red{\sf\:x\:=\:\dfrac{-\:1\:-\:\sqrt{-\:3}}{2}}}}$

Step-by-step-explanation:

The given quadratic equation is x² + x + 1 = 0.

Comparing with ax² + bx + c = 0, we get,

• a = 1
• b = 1
• c = 1

Now,

b² - 4ac = ( 1 )² - 4 * 1 * 1

⇒ b² - 4ac = 1 - 4

⇒ b² - 4ac = - 3

Now, we know that,

$\displaystyle{\pink{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^2\:-\:4ac}}{2a}}\sf\:\:\:-\:-\:-\:[\:Quadratic\:Formula\:]}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:1\:\pm\:\sqrt{-\:3}}{2\:\times\:1}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:1\:\pm\:\sqrt{-\:3}}{2}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:\dfrac{-\:1\:+\:\sqrt{-\:3}}{2}}}}\sf\:\:\:OR\:\:\:\underline{\boxed{\red{\sf\:x\:=\:\dfrac{-\:1\:-\:\sqrt{-\:3}}{2}}}}}$

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Additional Information:

1. Quadratic Equation:

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is ax² + bx + c = 0.

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula to solve quadratic equation:

$\displaystyle{\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}}$

Answer 2

The value of x is:

• -1+√-3÷2

or

• -1-√-3÷2

• Go through the attachment for the answer.