Question

3 x. 3x²+x-3=0 Find the zeros

Answer 1

Answer:

The zeroes of this polynomial are $x_{1} \approx 0.847$ and $x_{2} \approx -1.180$.

Step-by-step explanation:

Let $3\cdot x^{2}+x - 3 = 0$, the quickest and most efficient approach to find the zeroes of this second order polynomial is by Quadratic Formula. For all $a\cdot x^{2}+b\cdot x + c = 0$, roots are determined by:

$x_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$ (1)

Where $a$, $b$, $c$ are coefficients of the polynomial.

If we know that $a = 3$, $b = 1$ and $c = -3$, then roots of the polynomial are, respectively:

$x_{1,2} = \frac{-1\pm\sqrt{1^{2}-4\cdot (3)\cdot (-3)}}{2\cdot (3)}$

$x_{1,2} =\frac{-1\pm \sqrt{37}}{6}$

The zeroes of this polynomial are $x_{1} \approx 0.847$ and $x_{2} \approx -1.180$.