Math, asked by satindersingh4581, 1 year ago

Quadratic equation 2 x square minus root 5 x + 1 equal to zero has how many roots

Answers

Answered by Dhara19
29

Answer:

as it has 2 degree.. there are possibly 2 roots of the following equation.

Answered by pinquancaro
18

The quadratic equation 2x^2-\sqrt5x+1=0 has two imaginary roots i.e. x=\frac{\sqrt5+\sqrt{3}i}{4},\frac{\sqrt5-\sqrt{3}i}{4}

Step-by-step explanation:

Given : Quadratic equation 2x^2-\sqrt5x+1=0

To find : How many roots the quadratic equation has ?

Solution :

First we get the nature of roots,

In quadratic equation 2x^2-\sqrt5x+1=0

a=2, b=-\sqrt5 and c=1

The discriminant is D=b^2-4ac

D=(-\sqrt5)^2-4(2)(1)

D=5-8

D=-3<0

When D<0 the there are two imaginary roots.

Solve by quadratic formula,

x=\frac{-b\ \pm\ \sqrt{D}}{2a}

Substitute the values,

x=\frac{-(-\sqrt5)\pm\ \sqrt{-3}}{2(2)}

x=\frac{\sqrt5\pm\ \sqrt{3}i}{4}

x=\frac{\sqrt5+\sqrt{3}i}{4},\frac{\sqrt5-\sqrt{3}i}{4}

Therefore, the quadratic equation 2x^2-\sqrt5x+1=0 has two imaginary roots i.e. x=\frac{\sqrt5+\sqrt{3}i}{4},\frac{\sqrt5-\sqrt{3}i}{4}

#Learn more

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