How do you find the real solutions of the polynomial #14x^2+5=3x^4#?

1 Answer
Ujjwal
Jan 19, 2018

See below

Explanation:

# 14x^2 + 5 = 3x^4#
# 0 = 3x^4 - 14x^2 - 5#
# 0 = 3x^4 - 15x^2 + x^2 - 5#
# 0 = 3x^2(x^2-5) + 1(x^2-5)#
# 0 = (3x^2+1)(x^2-5)#

# 0 = 3x^2 + 1#
# -1 = 3x^2#
# -1/3 = x^2#
# +-sqrt(-1/3) = x#
These roots are not real.

#x^2 - 5 = 0#
#x^2 = 5#
#x = +-sqrt5#
These roots are real.

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