Question

State whether the following statements are true or false. Give reasons to justify your answers.

c) The polynomial √x4 4x +1 is a quadratic trinomial​

Answer 1

You get the number inside root when you square the root.

So, the square root of x⁴₊4x₊1 exists, it gives x⁴₊4x₊1 after squaring.

Suppose ax²+bx+c is the square root of x⁴₊4x₊1.

(ax²₊bx₊c)²=a²x⁴₊b²x²₊c²₊2(abx³+bcx+cax²)

=ax⁴₊2bx³₊2cax²₊b²x²₊2bcx+c²

ax⁴₊2bx³₊2cax²₊b²x²₊2bcx+c² is necessarily x⁴₊4x₊1.

By comparison of co-efficients

From x⁴ : a=1

From x³ : 2b=0 or b=0

From x² : 2ca+b²=0, since we are given value

→2c+0=0, or c=0

From x : 2bc=4, since we are given value

→ 0=4 (CONTRADICTION)

→Therefore, √x⁴₊4x₊1 doesn't exist. Hence shown.

I hope it helps. This is my first time solving the question.

Answer 2

Answer:

yay

Step-by-step explanation:

yay