Question

Find the zeros of the polynomial p(x) = 4x2 - 25

Answer 1

p(x) = 4x² - 25

4x² - 25 = 0

(2x)² - (5)² = 0

a²-b² = (a+b)(a-b)

(2x+5) (2x-5) = 0

2x+5 = 0 ; x = -5/2

2x-5 = 0 ; x = 5/2

The zeroes of the given polynomial are 5/2 and -5/2

Answer 2

Hello !

p(x) = 4x² - 25

p(x) = 0

 That is ,
4x² - 25 = 0
we can write this in the form a² - b²

(2x)² - (5)² = 0

we know that ,
a²-b² = (a+b)(a-b)
 so ,

(2x)² - (5)²  = (2x+5) (2x-5)

so ,
(2x+5) (2x-5) = 0

2x+5 = 0  ====>  x = -5/2

2x-5 = 0  ====>  x = 5/2


The zeroes of p(x) are 5/2 and -5/2