Question

for what values of x, the following expression are negative?

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Answer 1

Answer:

x^2–5x+14 = 0

solve the quadratic eqn ax^2+bx+c =0 .

since it is quadratic eqn, we will hav two x values.

x1 = -b + √(b^2–4ac)/2a → eqn 1

and

x2 = -b-√(b^2–4ac)/2a →eqn 2

here a=1, b=-5,c=14.

from eqn 1

x1 = (-(-5) + √(-5×-5)-(4×1×14))/2×1

= (5 + √(25–56))/2

= (5+ √-31)/2

x1= 2.5 + √-31/2

also from eqn 2

x2 = 2.5 - √-31/2

for both x values ,since square root of a negative number doesnt exist in the sets of real numbers.

therefore x value not belongs to R.