Question

Q-10` find the zeros of the polynomial `(x-2)^(2)-(x+3)^(2)​

Answer 1

Answer:

          -1/2

Step-by-step explanation:

Factorising here is easy if we use difference of squares: a²-b² = (a-b)(a+b).

So...

    (x - 2)² - (x + 3)²  =  0

⇒  [ (x-2)-(x+3) ] [ (x-2)+(x+3) ]  =  0

⇒  [ -5 ] [ 2x + 1 ]  =  0

⇒  2x + 1  =  0

⇒  x  =  -1/2

Alternatively

We could expand the squares...

    (x - 2)² - (x + 3)²  =  0

⇒  (x² - 4x + 4) - (x² + 6x + 9)  =  0

⇒  -10x - 5  =  0

⇒  10x  =  -5

⇒  x  =  -5/10

⇒  x  =  -1/2