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let f(x) = 3x^2 - 3x + 1. The roots of f is the same as asking for x where f(x) = 0.
So we do it f(x) = 0, 3x^2 - 3x + 1 = 0. Using "complete the square" method
3(x^2 - x) + 1 = 0
3(x^2 + (2 . - 1/2 . x) + (-1/2)^2 -(-1/2)^2) + 1 = 0
3(x - 1/2)^2 -3/4 + 1 = 0
3(x - 1/2)^2 + 1/4 = 0
By the quadratic formula, the solution comes out to be
x = [3+√(-3)]/6 and x = [3-√(-3)]/6
or
x = (3+i√3)/6 and x = (3-i√3)/6
in other words, the solutions are complex numbers.
What else can I help you with?
Which two values of x are roots of the polynomial x2 plus 5x plus 9?
-2.5 + 1.6583123951777i-2.5 - 1.6583123951777i
Which two values of x are roots of the polynomial below x2 plus 5x plus 11?
There are none because the discriminant of the given quadratic expression is less than zero.
X2-11x plus 13 has two values of x are roots of a polynomial what is it?
x=11+69/2 and x=11-69/2
Which two values of x are roots of the polynomial x2 plus 3x - 5?
To find the roots of the polynomial (x^2 + 3x - 5), we need to set the polynomial equal to zero and solve for x. So, (x^2 + 3x - 5 = 0). To solve this quadratic equation, we can use the quadratic formula: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}), where a = 1, b = 3, and c = -5. Plugging these values into the formula, we get (x = \frac{-3 \pm \sqrt{3^2 - 41(-5)}}{2*1}), which simplifies to (x = \frac{-3 \pm \sqrt{29}}{2}). Therefore, the two values of x that are roots of the polynomial are (x = \frac{-3 + \sqrt{29}}{2}) and (x = \frac{-3 - \sqrt{29}}{2}).
What kind of polynomial is this 2x5 plus 2x4 plus 2x plus 1?
A fifth degree polynomial.
Which two values of x are roots of the polynomial x2 plus 5x plus 9?
-2.5 + 1.6583123951777i-2.5 - 1.6583123951777i
Which two values of x are roots of the polynomial below x2 plus 5x plus 11?
There are none because the discriminant of the given quadratic expression is less than zero.
What 2 values of x are roots of the polynomial x2 plus 3x-5?
You can find the roots with the quadratic equation (a = 1, b = 3, c = -5).
Which two values of x are roots of the polynomial below x2 plus 5x plus 9?
x = -2.5 + 1.6583123951777ix = -2.5 - 1.6583123951777iwhere i is the square root of negative one.
The polynomial 32 plus 4x plus 3 has how many roots?
1
X2-11x plus 13 has two values of x are roots of a polynomial what is it?
x=11+69/2 and x=11-69/2
If the factors of a polynomial are x plus 2 and x plus 6 what values of x make that polynomial 0?
-2 and -6
What are the roots of the polynomial x2 plus 3x plus 5?
You can find the roots with the quadratic equation (a = 1, b = 3, c = -5).
The polynomial 4x2 plus 5x plus 4 has how many roots?
None, it involves the square root of a negative number so the roots are imaginary.
If the factors of a polynomial are x plus 4 and x plus 8 what values of x make that polynomial 0?
-6 Check: -6+4-6+8 = 0
What is 4x squared plus 16x plus 15?
The expression (4x^2 + 16x + 15) is a quadratic polynomial. It can be factored into ((2x + 3)(2x + 5)). Alternatively, it can be analyzed using the quadratic formula to find its roots or solved for specific values of (x).
What is the discriminant in the polynomial x2 plus 4x plus 5?
It is: 16-20 = -4 which means that the given quadratic expression has no real roots.
