Question

2m²-5m=0,m=2,5/2 Determine whether the values given against each of the quadratic equation are the roots of the equation.

Answer 1

Solution:-

given by quadratic equation:-

$2 {m}^{2} - 5m = 0 \\ m(2m - 5) = 0 \\ m = 0 \\ m = \frac{5}{2}$
●here , m =( 0 , 5/2)

●the given values of m = 2 , does not exits

●x = 5/2 is the root of given equation (2m²-5m=0) . ans

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Answer 2

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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