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For what value(s) of k will the equation kx2-5x+k = 0 have a repeated root?
- a)±5/2
- b)5/2
- c)-5/2
- d)3/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
For what value(s) of k will the equation kx2-5x+k = 0 have a repeated ...
Kx^2-5x+k=0
a=k, b=-5, c=k
b^2-4ac=0
(-5)^2 - 4×k×k= 0
25 - 4k^2 = 0
25/4 = k^2
+√25/4 = k
-
+-5/2 ANS.
a=k, b=-5, c=k
b^2-4ac=0
(-5)^2 - 4×k×k= 0
25 - 4k^2 = 0
25/4 = k^2
+√25/4 = k
-
+-5/2 ANS.
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Community Answer
For what value(s) of k will the equation kx2-5x+k = 0 have a repeated ...
The equation kx^2 - 5x + k = 0 will have a repeated root if and only if the discriminant is equal to zero.
The discriminant is given by b^2 - 4ac, where a = k, b = -5, and c = k.
So, we have (-5)^2 - 4(k)(k) = 0.
Simplifying, we get 25 - 4k^2 = 0.
Rearranging, we have 4k^2 = 25.
Dividing both sides by 4, we get k^2 = 25/4.
Taking the square root of both sides, we have k = ±5/2.
Therefore, the equation will have a repeated root when k = 5/2 or k = -5/2.
Answer: a) k = 5/2 or k = -5/2.
The discriminant is given by b^2 - 4ac, where a = k, b = -5, and c = k.
So, we have (-5)^2 - 4(k)(k) = 0.
Simplifying, we get 25 - 4k^2 = 0.
Rearranging, we have 4k^2 = 25.
Dividing both sides by 4, we get k^2 = 25/4.
Taking the square root of both sides, we have k = ±5/2.
Therefore, the equation will have a repeated root when k = 5/2 or k = -5/2.
Answer: a) k = 5/2 or k = -5/2.
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