Question

check the nature of roots of the equation x^2-4x+3root2=0

Answer 1

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HERE IS YOUR ANSWER

Answer 2

The nature of the roots is imaginary and unequal.

Given:

$x^{2}$-4x+3√2=0

To find:

The nature of roots

Solution:

The value of the discriminant will determine the roots' nature.

The given equation: $x^{2}$-4x+3√2=0

Here, the coefficient of $x^{2}$ is 1, of x is -4 and the constant term is 3√2.

So, a=1, b= -4, and c=3√2.

The discriminant, D=$b^{2}$-4ac

Using values,

D=$(-4)^{2}$-4(1)(3√2)

D=16-12√2

Using √2=1.414,

D=16-12(1.414)

D=16-16.96

D= -0.96

The value of D<0 or negative.

The roots are imaginary and unequal.

Therefore, the nature of the roots is imaginary and unequal.