find the value of k if the given equation has equal roots x^2-2(k+1)x+k^2=0
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find the value of k if the given equation has equal roots x^2-2(k+1)x+k^2=0
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Answer:
Given:
To find:
Solution:
The given quadratic equation is x²-2(k+1)x+k²=0
Here, a = 1, b = -2(k+1) and c = k²
If a quadratic equation has equal roots then
D=0
=> b²- 4ac = 0
=> [-2(k+1)]² - 4(1)(k²) = 0
=> 4(k+1)² - 4k² = 0
=> 4(k²+2k+1) - 4k² = 0
=> 4k² + 8k + 4 - 4k² = 0
=> 8k = -4
=> k = -4/8
=> k = -1/2
The value of k is -1/2.