Question

determine the nature of the roots of the equation x²-4x+2=0​

Answer 1

Answer:

Roots of the equation is unequal and real.

Explanation:

Given equation,

$\rm \implies \: {x}^{2} - 4x + 2 = 0$

Where, we need to determine the nature of the roots

On comparing the equation with the general form of a quadratic equation i.e., ax² + bx + c = 0

We get,

• a = 1
• b = -4
• c = 2

Now ,

Finding it's discriminant :-

$\rm \longrightarrow \: d = {b}^{2} - 4ac$

$\rm \longrightarrow \: d = { (- 4)}^{2} - 4(1)(2)$

$\rm \longrightarrow \: d = 16 - 8$

$\rm \longrightarrow \: d = 8$

$\rm \therefore \: discriminant \: of \: the \: polynomial \: is \: = 8$

Since, 8 > 0

∴ Nature of roots of the equation is unequal and real

________________________

Determination of nature of roots:

• When the discriminant is greater than zero then the roots are unequal and real.
• When the is zero then the nature of roots is equal and real.

Answer 2

Answer:-

$\\ \sf\longmapsto x^2-4x+2=0$

• a=1
• b=-4
• c=2

Lets find Discriminant

$\\ \sf\longmapsto D=b^2-4ac$

$\\ \sf\longmapsto D=(-4)^2-4(1)(2)$

$\\ \sf\longmapsto D=16-8$

$\\ \sf\longmapsto D=8$

Here

• D>0
• D is not a perfect square.

Hence

• The roots of the equation are real and unequal and irrational.