Question

X^6+3x^3-5
write the expression in quadratic form

Answer 1

To write the expression x^6+3x^3-5 in quadratic form, we substitute x^3 with a new variable y. By comparing the coefficients in the quadratic form y^2 + 3y - 5 with the general form ax^2 + bx + c, we determine a=1, b=3, and c=-5. We can then use the quadratic formula to find the solutions for x.

Step-by-step explanation:

To write the expression x^6+3x^3-5 in quadratic form, we can substitute x^3 with a new variable, say y. Let's rewrite the expression as y^2 + 3y - 5. Now, we have a quadratic equation which can be easily solved using various methods such as factoring, completing the square, or using the quadratic formula.

In this case, the expression cannot be factored easily, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

By comparing the coefficients in the quadratic form y^2 + 3y - 5 with the general form ax^2 + bx + c, we can determine that a = 1, b = 3, and c = -5.

Substituting these values into the quadratic formula, we can find the solutions for x.

Answer 2

Step-by-step explanation:

`v = {x}^(3) \\ {v}^(2) + 3v - 5 = 0 \\`

Solving this equation using the quadratic formula, we get two real solutions :

1.1926 or -4.1926

Now we know the values of v , we can calculate x since x is ∛ v

`{x}^(6) + 3 {x}^(3) - 5 = 0`

`x = \sqrt[3]{1.1926} = 1.0605 \\ x = \sqrt[3]{ - 4.1926} = - 1.6125`