Question

The real number k for which 2x3+3x+k=0 has two distinct real roots

Answer 1

f(x) = 2x^3+3x+k

f′(x) = 6x^2+3

f′(x) = 0

x^2 = -1/2

Not Possible.

As condition for two distinct real root is = 0

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Answer 2

Given equation :- 2x² + 3x + k = 0

• When the quadratic equation have distinct real roots then the discriminant will be greater than Zero .

i.e, D > 0

And

D = b² - 4ac

So, here ,

b² - 4ac > 0

( 3 )² - 4 × 2 × k > 0

9 - 8k > 0

9 > 8k

9/8 > k

The value of k will satisfy the equation only when the value is less than 9/8