Question

p(x)=x²+2x+1 has two distinct zeros.State whether the given statement is true or false.

Answer 1

Acc to the question, the given polynomial is quadratic in nature.

The polynomial P(x)=x²+2x+1 can be resolved as below:

P(x) = x²+2x+1 = x² + x + x + 1

or, x(x + 1) + 1(x + 1)

or, (x+1) * (x + 1)

Therefore, it is pretty obvious that it'll have one distinct zero. i.e. -1 therfore, the given statement is false.

Answer 2

Dear Student,

Answer: Statement is wrong.

Solution:

let us solve the given polynomial ,to find zeros

by factor theorem

${x}^{2} + 2x + 1 = 0 \\ \\ {x}^{2} + x + x + 1 = 0 \\ \\ x(x + 1) + 1(x + 1) = 0 \\ \\ (x + 1) (x + 1) = 0 \\ \\ x + 1 = 0 \\ \\ x = - 1$
So ,both the zeros are same.

Another method :

If Determinant D = 0
$\sqrt{ {b}^{2} - 4ac }$
by compare the equation with standard equation we get the value of a,b and c

Standard equation

$a {x}^{2} + bx + c = 0$
$a = 1 \\ \\ b = 2 \\ \\ c = 1$

D =
$\sqrt{ {b}^{2} - 4ac } \\ \\ = \sqrt{ {2}^{2} - 4 \times 1 \times 1} \\ \\ = \sqrt{4 - 4} \\ \\ = 0$
That means Quadratic equation has same roots.

Thus the given statement is wrong.

Hope it helps you.

Thank you