Question

the roots of the equation root 2 x square - 2 x minus root 3 is equal to zero are​

Answer 1

The roots of given quadratic equation is 3 , -1  .

Step-by-step explanation:

Given as :

The quadratic equation

2 x² - 2 x - √3  = 0

Let The roots of this equation = a , b

Now, According to question

The standard quadratic equation

a x² + b x + c  = 0.

So,  The roots of equation can be determine by formula

x = $\dfrac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Now, comparing standard with given quadratic equation

Or,  x = $\dfrac{-(-2)\pm \sqrt{(-2)^{2}-4\times 2\times (-\sqrt{3})}}{2\times 1}$

Or,  x = $\dfrac{2\pm \sqrt{2-4\times 2\times (-\sqrt{3})}}{2}$

Or,  x = $\dfrac{2\pm \sqrt{2+8\times\sqrt{3}}}{2}$

Or, The roots = a , b = x = $\dfrac{2\pm \sqrt{2+8\times\sqrt{3}}}{2}$

i.e   a = $\dfrac{2+\sqrt{2+8\times\sqrt{3}}}{2}$                            b = $\dfrac{2-\sqrt{2+8\times\sqrt{3}}}{2}$

Or,  a = $\dfrac{2+\sqrt{15.8} }{2}$                                        b = $\dfrac{2-\sqrt{15.8} }{2}$

Or, a = $\dfrac{2+4}{2}$                                                 b = $\dfrac{2-4}{2}$

∴   a = 3                                                        b = - 1

So, The roots of given quadratic equation = a , b = 3 , -1

Hence, The roots of given quadratic equation is 3 , -1  . Answer

Answer 2

Step-by-step explanation:

Given as :

The quadratic equation

2 x² - 2 x - √3 = 0

Let The roots of this equation = a , b

Now, According to question

The standard quadratic equation

a x² + b x + c = 0.

So, The roots of equation can be determine by formula

x = \dfrac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}

2×a

−b±

b

2

−4×a×c

Now, comparing standard with given quadratic equation

Or, x = \dfrac{-(-2)\pm \sqrt{(-2)^{2}-4\times 2\times (-\sqrt{3})}}{2\times 1}

2×1

−(−2)±

(−2)

2

−4×2×(−

3

)

Or, x = \dfrac{2\pm \sqrt{2-4\times 2\times (-\sqrt{3})}}{2}

2

2±

2−4×2×(−

3

)

Or, x = \dfrac{2\pm \sqrt{2+8\times\sqrt{3}}}{2}

2

2±

2+8×

3

Or, The roots = a , b = x = \dfrac{2\pm \sqrt{2+8\times\sqrt{3}}}{2}

2

2±

2+8×

3

i.e a = \dfrac{2+\sqrt{2+8\times\sqrt{3}}}{2}

2

2+

2+8×

3

b = \dfrac{2-\sqrt{2+8\times\sqrt{3}}}{2}

2

2−

2+8×

3

Or, a = \dfrac{2+\sqrt{15.8} }{2}

2

2+

15.8

b = \dfrac{2-\sqrt{15.8} }{2}

2

2−

15.8

Or, a = \dfrac{2+4}{2}

2

2+4

b = \dfrac{2-4}{2}

2

2−4

∴ a = 3 b = - 1

So, The roots of given quadratic equation = a , b = 3 , -1

Hence, The roots of given quadratic equation is 3 , -1 . Answer

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