Math, asked by Anonymous, 5 months ago

find the smallest integer value of k for which 2x² + 5x + 3k is always positive for all real value of x

Answers

Answered by palakgupta2395
2

Answer:

You need write x^2+ka+k = 0 has 2 distinct real roots. Only an equation has roots & an expression like x^2+kx+k does not have any roots. Now for amswer -

The discriminant b^2–4ac of the equation is k^2–8k. This must be > 0

So k(k-8) >0. It can happen if both the terms k, k-8 are < 0 OR when both are >0

Both are less than zero

k<0 and k-8<0 => k<0 and k<8 or k<0 (lower of the values)

Both are > 0

k>0 and k-8>0 => k>8

The result is when k <0 or k>8 the roots are real and distinct

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