Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
Answers
Answer:
Yes quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1
Hey there !
Solution:
For a Quadratic Equation to have equal roots, it must satisfy the condition:
b² - 4ac = 0
Given equation is x² + kx + k = 0
a = 1, b = k, x = k
So Substituting in the equation we get,
=> k² - 4 ( 1 ) ( k ) = 0
=> k² - 4k = 0
=> k ( k - 4 ) = 0
=> k = 0 , k = 4
But in the question, it is given that k is greater than 1.
Hence the value of k is 4 if the equation has common roots.
Hence if the value of k = 4, then the equation ( x² + kx + k ) will have equal roots.
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OR
NO.
For the roots to be equal in,
x2 + kx + k,
we must have the discreminant zero.
i.e. k2 - 4k = 0
and this gives,
k = 4.
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