Question

Y equal to x square - 2 x square - 3 and find the zeros​

Answer 1

Answer:

By factorisation method:-

The given polynomial is :

=> y = x^2 - 2x - 3

=> y = x^2 - 3x + x - 3

=> y = x(x - 3) + (x - 3)

=> y = (x - 3)(x + 1)

To find the zeros of the given polynomial, equate it to zero.

Thus;

=> y = 0

=> (x - 3)(x + 1) = 0

Case:(1)

when, (x - 3) = 0

=> x = 3

Case:(2)

when, (x + 1) = 0

=> x = -1

Thus,

The zeros of the given polynomial are :

-1 and 3.

Finding zeros using quadratic formula:

Note:

If we consider a quadratic polynomial in variable x, say : y = p(x) = ax^2 + bx + c

Then , the zeros of the polynomial is given by;

x = [ -b ± √(b^2 - 4•a•c) ]/2•a

Here, the given polynomial is:

y = x^2 - 2x - 3

Clearly, here we have;

a = 1

b = -2

c = -3

Thus, putting these in quadratic formula we get;

=> x = [ -b ± √(b^2 - 4•a•c] }/2•a

=> x = [ -(-2) ± √{(-2)^2 - 4•1•(-3)} ]/2•1

=> x = [ 2 ± √{4 + 12} ]/2

=> x = [ 2 ± √{16} ]/2

=> x = [ 2 ± 4 ]/2

=> x = [ 1 ± 2 ]

Case:(1)

when, x = 1 + 2

=> x = 3

Case:(2)

when, x = 1 - 2

=> x = -1

Thus, the zeros of the given polynomial are: 3 and -1.