Question

[ √ {2x^2} + √ {3x} = 0 ]

a) ( x = 0 )

b) ( x = -{3}/{2} )

c) ( x = {3}/{2} )

d) ( x = {3}-{2} )

Answer 1

The correct answer to the equation √{2x^2} + √{3x} = 0 is a) (x = 0), because each term within the square roots must individually equal zero for the entire expression to equal zero.

Step-by-step explanation:

The student's question involves solving a given equation: √{2x^2} + √{3x} = 0. To find the value of x, we note that for the expression to be equal to zero, each individual square root term must be zero because square roots of non-negative numbers are always non-negative. This implies 2x^2 must be 0 and 3x must also be 0.

Setting each term within the square root to zero gives:

• 2x^2 = 0 → x = 0
• 3x = 0 → x = 0

Both terms give the same solution, x = 0. Hence, the correct answer is a) (x = 0).