Question

if 3x²-kx-4=0 has roots equal in magnitude but opposite in sign then k=​

Answer 1

Answer:

By theory of location of roots,

If roots are equal in magnitude but opposite in sign,

Then zero lies between both roots.

For this, we have af(0)<0

3f(0)<0

f(0)<0

Substituting x = 0 in the expression

-4 < 0

Which is always true

Now for equal roots, we have to equate discriminant to zero.

D = b² - 4ac = 0

D = k² + 48 = 0

k² = -48

Which has no real solution.

Therefore k has no real solution i.e k ∈ Ф

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