The real number K for which the equation, 2x^2+3x+k=0 has two distinct real roots in [0,1]

belandong0ir

belandong0ir

Answered question

2022-12-28

The real number K for which the equation, 2x3+3x+k=0 has two distinct real roots in [0,1]
A) lies between 1 and 2
B) lies between 2 and 3
C) lies between -1 and 0
D) does not exist

Answer & Explanation

popol48w

popol48w

Beginner2022-12-29Added 6 answers

The correct answer is D does not exist
Compute the value:
Let f(x)=2x3+3x+k
Differentiate with respect to x,
f'(x)=6x2+3
For all x belongs to 0,1, f'(x)>0.
Since f(x) is a strictly increasing function.
Thus, f(x)=0 has a single real root.
Thus, two distinct real roots are impossible.
Therefore, option (D) is the correct option.

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