Question

find the roots of the quadratic formula if they exist by using quadratic formula x²-4x-1=0​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Solution :

$\large\sf x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

Here

• a = 1
• b = - 4
• c = - 1

Substitute values in formula

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

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$\sf x = \dfrac{4 \pm \sqrt{16 + 4} }{2}$

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$\sf x = \dfrac{4 \pm \sqrt{20} }{2}$

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Taking +ve sign

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$\sf x = \dfrac{4 + \sqrt{20} }{2} = 2+\sqrt{5}$

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Taking -ve sign

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$\sf x = \dfrac{4 - \sqrt{20} }{2} = 2- \sqrt{5}$

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Roots of given equation are 2 + √5 and 2 - √5