Find all real and/or imaginary solutions.
X^4+5x-14=0
To find all real and/or imaginary solutions for the equation x^4 + 5x - 14 = 0, we can use the method of factoring or the quadratic formula. In this case, factoring is not straightforward, so we will use the quadratic formula.
The equation x^4 + 5x - 14 = 0 can be rewritten in standard form as x^4 + 0x^3 + 5x^2 + 0x - 14 = 0.
By comparing this to the general quadratic equation ax^2 + bx + c = 0, we have:
a = 1, b = 5, c = -14.
The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / 2a.
Plugging in the values of a, b, and c, we get:
x = (-5 ± √(5^2 - 4*1*(-14))) / (2*1)
x = (-5 ± √(25 + 56)) / 2
x = (-5 ± √81) / 2
x = (-5 ± 9) / 2
This gives us two possible solutions:
x = (-5 + 9) / 2 = 4 / 2 = 2
x = (-5 - 9) / 2 = -14 / 2 = -7
Therefore, the real solutions to the equation x^4 + 5x - 14 = 0 are x = 2 and x = -7.