Question

factorise X square + x square + 1

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Answer 1

Given,

Quadratic equations is x^2 + x^2 +1

Now, we to factorise the given quadratic equation we put=>

2x^2 + 1 =0

Now, we will use discriminant to find the nature of its roots.

We know,

discriminant,d= b^2 - 4ac

=>d = 0 - 4×(2)×(1)

=>d = -4

=>d<0

But when d <0 then no real roots are possible for the equation and it wil have roots as imaginery numbers.

Hence the factorisation of x^2 + x^2 +1 is not possible as the roots are not real.

Remember

When =>

1)discriminant =0

then roots are real and equal roots

2)discriminant <0

then the roots are imaginery and not possible.

3) discriminant >0

then the roots are real and distinct

Answer 2

The given expression is :-

x² + x² + 1

⇒ 2 x² + 1

This is a typical quadratic equation .

We can check whether an equation is quadratic or not by seeing the highest power .

Here the degree or the highest power is 2 .

Hence it is quadratic in nature .

Let the above equation be equated with 0 :-

2 x² = - 1

⇒ x² = - 1/2

⇒ x = i/√2

⇒ x = √2i/2

Hence the value of x will be imaginary .

Another way to check this is by discriminant method .

Let 2 x² + 1 be compared with ax² + bx + c :

a = 2

b = 0

c = 1

Hence b² = 0

4 ac = 8

Since b² < 4 ac , we cannot have a real solution .

∴ The given equation cannot be factorised .

NOTE :

When b² = 4 ac , the roots are real , equal .

When b² > 4 ac roots are real , unequal .

b² - 4 ac is called discriminant .