Question

can the quadratic equation x^2+kx+k=0 have equal roots for some odd integer k>1​

Answer 1

Answer:

no ,this condition is not possible.

I hope the attached pic would help you

Answer 2

Answer:No

Solution:

For Quadratic equations to be equal roots

D = 0

ie

${b}^{2} - 4ac = 0$
Here in the given equation as compared to the standard Quadratic equation

$a \: = 1 \\ \\ b = k \\ \\ c \: = k$
So

${k}^{2} - 4k = 0 \\ \\ k(k - 4) = 0 \\ \\ so \: either \: k = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4$
So, the given Quadratic equation has real and equal roots if either k = 0 or k = 4.

So it doesn't satisfy the given condition,since 4 is not an odd number.

Hope it helps you.