Question

Find zeros of the polynomial 3x^2-75

Answer 1

Answer:

Required zeroes of this polynomial are 5 and - 5.

Step-by-step explanation:

If we want to get the zeroes, polynomial must be equal to 0. Thus,

= > 3x^2 - 75 = 0

Adding 75 on both sides of this equation :

= > 3x^2 - 75 + 75 = 0 + 75

= > 3x^2 = 75

Dividing both sides by 3 :

= > 3x^2 / 3 = 75 / 3

= > x^2 = 25

= > x = ±√25

= > x = ±√( 5 )

= > x = ± 5

Hence the required zeroes of this polynomial are 5 and - 5.

Answer 2

Answer:

We have

3x^2 - 75

= 3×x^2 - 3×25

Taking '3' common, we have

= 3(x^2 - 25)

Using the formula

a^2 - b^2 = (a+b)(a-b), we have

= 3(x^2 - 5^2)

= 3(x+5)(x-5)

So,

The polynomial 3x^2 - 75 can be written as 3(x+5)(x-5) and this whole value will become zero when either x+5 = 0 "OR" x-5 = 0 because 3 can never be equal to zero.

Which means x = -5 "OR" x = 5.

i.e., when x = -5 "OR" x = 5, the polynomial will become zero.

So x = 5 & x = -5 are two zeros of the polynomial.