Question

For which of the following values of p will the solutions to the equation 2x^2+p=0 be complex numbers?

a) -50
b) -14
c) -7/2
d) 0
e) 32

Answer 1

The answer is 32.

Explanation:

Complex numbers are the number that can be written in the form of a + bi, where a is the real part, b is the imaginary part and i is the unit imaginary part which is equal to √-1.

Solving the given equation:

2x^x + p = 0

2x^2/2 + p/2 = 0/2

x^2 + p/2 = 0

x^2 +p/2 -p/2 = -p/2

x^2 = -p/2

taking √ on both sides

√x^2 =√(-p/2)

x = √(-1)(p/2)

as we know that √(-1) = i

therefore

x = √(p/2)i

Hence, form the given choices only 32 will gives the complex number as a solution.

Now putting p = 32, we'll get

x = √(32/2)i

x = 4i is the required solution.