Question

Write a qua
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3. Determine the roots of the equation √3 x2 - 2x - √3 = 0​

Answer 1

Question :

Determine the roots of the equation : √3x²-2x-√3=0.

Solution :

We'll find the roots of the equation by splitting the middle term :

→ √3x²-2x-√3=0

→ √3x²+1x-3x-√3=0

→ x(√3x+1) -√3(√3x+1)=0

→ (x-√3) (√3x+1)=0

• x-√3=0

→ x=+√3

• √3x+1=0

→ x=-1/√3

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Therefore, the roots of the quadratic equation √3x²-2x-√3=0 are √3 and -1/√3.

Answer 2

√3 and -1/√3

Step-by-step explanation:

Given:

• A quadratic equation: √3x²-2x-√3 = 0

To find:

• Roots of the equation.

Solution:

By factorization method, we can solve the given quadratic equation and find their roots.

$\implies{\rm}$ √3x²-2x-√3 = 0

-2x can be spliited as -3x+x on the basis of sum-product pattern.

$\implies{\rm}$ √3x²-3x+x-√3 = 0

Let us take √3x and 1 as common factor from the pairs.

$\implies{\rm}$ √3x(x-√3)+1(x-√3) = 0

Let us write the given equation in factorized form.

$\implies{\rm}$ (√3x+1)(x-√3) = 0

$\implies{\rm}$ (√3x+1)=0 or (x-√3)=0

$\implies{\rm}$ √3x = -1 or x = √3

$\implies{\rm}$ x = -1/√3 or x = √3

Hence, the roots of the quadratic equation are √3 and -1/√3.