the number of integral value of 'm' is less than 50, so that the roots of the quadratic equation mx2+(2m-1)x+(m-2)=0 are rational,are. A) 6. B)7. C)8. D)none of these
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Answer:
Option A is correct.
Step-by-step explanation:
Given Quadratic Equation:
mx² + (2m+1)x + (m-2) = 0
To find: Number of value of m for which roots are rational and m < 50.
We know the roots are rational if the Value of the discriminant is a perfect square number.
D = b² - 4ac
= (2m-1)² - 4(m)(m-2)
= 4m² + 1 - 4m - 4m² + 8m
= 4m + 1
For the roots to be rational 4m + 1 should be a perfect square.
4m + 1 to be perfect square value of m = 2 , 6 , 12 , 20 , 30 and 42
Therefore, Option A is correct.
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