Question

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

Answer 1

Answer:

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

Answer 2

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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