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If x=m is one of the solutions of the equation 2x2+5x-m=0 the possible values of m are
- a)(0, 2)
- b)(0, -2)
- c)(0, 1)
- d)(1, -1)
Correct answer is option 'B'. Can you explain this answer?
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If x=m is one of the solutions of the equation 2x2+5x-m=0 the possible...
Ans.
Option (b)
If x = m is a solution of 2
+ 5x - m = 0, then
we can write given equation as,
2m2 + 5m - m = 0
⇒⇒ 2m2 + 4m = 0
⇒⇒ 2m (m + 2) = 0
⇒⇒ 2m = 0 or m + 2 = 0
⇒⇒ m = 0 or m = - 2
Thus, (0, -2) is the solution set for the same.
+ 5x - m = 0, thenwe can write given equation as,
2m2 + 5m - m = 0
⇒⇒ 2m2 + 4m = 0
⇒⇒ 2m (m + 2) = 0
⇒⇒ 2m = 0 or m + 2 = 0
⇒⇒ m = 0 or m = - 2
Thus, (0, -2) is the solution set for the same.
Most Upvoted Answer
If x=m is one of the solutions of the equation 2x2+5x-m=0 the possible...
Solution:
Given, x=m is one of the solutions of the equation 2x^2 + 5x - m = 0
We know that if x=m is one of the solutions of the equation, then (x-m) is a factor of the equation.
Using this property, we can write the equation as:
2x^2 + 5x - m = 2x^2 - 2mx + 7x - m
= 2x(x - m) + (7x - m)
= (x - m)(2x + 7)
Now, we have two factors of the equation: (x - m) and (2x + 7)
If x=m is one of the solutions of the equation, then (x - m) = 0
=> x = m
So, the other solution of the equation is given by (2x + 7) = 0
=> x = -7/2
Therefore, the solutions of the equation are x = m and x = -7/2
Now, we can substitute x = m in the equation (2x^2 + 5x - m = 0) to get:
2m^2 + 5m - m = 0
=> 2m^2 + 4m = 0
=> 2m(m + 2) = 0
So, the possible values of m are:
m = 0 or m = -2
But, we know that x = m is one of the solutions of the equation.
So, if x = m = 0, then the other solution of the equation is x = -7/2, which is not possible as it is not in the given range of options.
Therefore, the possible values of m are:
m = -2
or
m = 0
Hence, the correct answer is option 'B' (0, -2).
Given, x=m is one of the solutions of the equation 2x^2 + 5x - m = 0
We know that if x=m is one of the solutions of the equation, then (x-m) is a factor of the equation.
Using this property, we can write the equation as:
2x^2 + 5x - m = 2x^2 - 2mx + 7x - m
= 2x(x - m) + (7x - m)
= (x - m)(2x + 7)
Now, we have two factors of the equation: (x - m) and (2x + 7)
If x=m is one of the solutions of the equation, then (x - m) = 0
=> x = m
So, the other solution of the equation is given by (2x + 7) = 0
=> x = -7/2
Therefore, the solutions of the equation are x = m and x = -7/2
Now, we can substitute x = m in the equation (2x^2 + 5x - m = 0) to get:
2m^2 + 5m - m = 0
=> 2m^2 + 4m = 0
=> 2m(m + 2) = 0
So, the possible values of m are:
m = 0 or m = -2
But, we know that x = m is one of the solutions of the equation.
So, if x = m = 0, then the other solution of the equation is x = -7/2, which is not possible as it is not in the given range of options.
Therefore, the possible values of m are:
m = -2
or
m = 0
Hence, the correct answer is option 'B' (0, -2).
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