Question

Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?

Answer 1

Answer:

Yes quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1

Answer 2

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.

Hope my answer helped !

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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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