Question

Find a quadratic polynomial with integer coefficients which has x = 2/9, ± SQRT23/9 as its real zeros.

Answer 1

Answer:

The quadratic polynomial with integer coefficients is $y = 81\cdot x^{2}-36\cdot x -19$.

Step-by-step explanation:

Statement is incorrectly written. Correct form is described below:

Find a quadratic polynomial with integer coefficients which has the following real zeros: $x = \frac{2}{9}\pm \frac{\sqrt{23}}{9}$.

Let be $r_{1} = \frac{2}{9}+\frac{\sqrt{23}}{9}$ and $r_{2} = \frac{2}{9}-\frac{\sqrt{23}}{9}$ roots of the quadratic function. By Algebra we know that:

$y = (x-r_{1})\cdot (x-r_{2}) = x^{2}-(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2}$ (1)

Then, the quadratic polynomial is:

$y = x^{2}-\frac{4}{9}\cdot x -\frac{19}{81}$

$y = 81\cdot x^{2}-36\cdot x -19$

The quadratic polynomial with integer coefficients is $y = 81\cdot x^{2}-36\cdot x -19$.