Question

Verify whether the following on zero of the polynomial, indicated against them. p(x)=3x+1,x=-1/3

Answer 1

Given :

• p(x) = 3x + 1

To Find :

• If the number is the zero of given polynomial.

Solution :

As we have already been told about the value of x we will just substitute the value in the given polynomial and simplify it in order to know that if the given number is a zero of the polynomial.

↝p(x) = 3x + 1

↝p(-⅓) = 3(-⅓) + 1

↝p(-⅓) = $\small{\sf{\cancel{3} \times \dfrac{-1}{\cancel{3}}}}$ + 1

↝p(-⅓) = -1 + 1

☞p(-⅓) = 0

So , -⅓ is a zero of the given polynomial.

Supplementary information :

• A number which when substituted in the value of x and when simplified if gives the the final outcome as zero the number which were substituted is called as zero of the polynomial.

• When a negative and a positive are added they lead of negative and sign of Bigger number if the numbers aren't same :

☞-3 + 7 = 4

• When two same numbers one having negative value and one having positive value added or subtracted the whole gives us 0

☞ -10 + 10 = 0

Answer 2

We have

• p(x) = 3x + 1
• x= -1/3

So, we will put up the value of x in the p(x) and if the result so obtained is zero, it is the zero of polynomial i.e in simpler words of we subsitute the values of x in the polynomial and the result is zero, then it is said to be zero of Polynomial.

So, let's subsitute

→ p(x) = 3x + 1

→ p(-⅓) = 3x + 1

→ p(-⅓) = 3 × -⅓ + 1

→ p(-⅓) = 1 × -1 + 1

Note :- Remember the BODMAS rule.

→ p(-⅓) = -1 + 1

→ p(-⅓) = 0

Thus, we got zero

Hence, verified that 3x + 1 is the zero of polynomial x = -⅓