Question

Determine whether m = 2/5 is the root of the equation 2m2 - 5m = 0.The given equation is 2m2 - 5m = 0​

Answer 1

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METHOD TO CHECK WHETHER THE GIVEN VALUE IS A ZERO OF A POLYNOMIAL OR NOT:

If a polynomial in one variable (x) is given to us and a value of variable (x = c) is also given then to check that a value of x is a zero of given polynomial or not, we use the following steps.

•Put x = c in given polynomial and find the value of p(c).

• If p(c)= 0 , then x = c will be a zero of given polynomial and if p(c) ≠ 0, then x= c will not be a zero of a given polynomial.

SOLUTION :

Let p(m) = 2m²-5m=0..........(1)

On Putting m = 2 in eq 1

2m²-5m=0

2(2)² - 5(2) = 0

2×4 -10 = 0

8 -10 = 0

-2 ≠0

Here, m =2 is not the root of p(m).

On Putting m = 5/2 in eq 1.

2m²-5m=0

2(5/2)² - 5(5/2) = 0

2 (25/4) - 25/2 = 0

25/2 - 25/2 = 0

Here, p(5/2) = 0

Hence,p= 2 is not the root of the given equation & p = 5/2 is the root of the Given equation.

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Answer 2

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METHOD TO CHECK WHETHER THE GIVEN VALUE IS A ZERO OF A POLYNOMIAL OR NOT:

If a polynomial in one variable (x) is given to us and a value of variable (x = c) is also given then to check that a value of x is a zero of given polynomial or not, we use the following steps.

•Put x = c in given polynomial and find the value of p(c).

• If p(c)= 0 , then x = c will be a zero of given polynomial and if p(c) ≠ 0, then x= c will not be a zero of a given polynomial.

SOLUTION :

Let p(m) = 2m²-5m=0..........(1)

On Putting m = 2 in eq 1

2m²-5m=0

2(2)² - 5(2) = 0

2×4 -10 = 0

8 -10 = 0

-2 ≠0

Here, m =2 is not the root of p(m).

On Putting m = 5/2 in eq 1.

2m²-5m=0

2(5/2)² - 5(5/2) = 0

2 (25/4) - 25/2 = 0

25/2 - 25/2 = 0

Here, p(5/2) = 0

Hence,p= 2 is not the root of the given equation & p = 5/2 is the root of the Given equation.

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