By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
A value of x is a zero of a polynomial if and only if [tex]\sum\limits_{i=0}^{n} c_{i}\cdot x^{i} = 0[/tex], the quadratic formula for second order polynomials of the form a · x² + b · x + c = 0 is presented below:
[tex]x =\frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
If we know that a = 1, b = -20 and c = 32, then the roots of the second order polynomial are:
[tex]x = \frac{20 \pm \sqrt{(-20)^{2}-4\cdot (1)\cdot (32)}}{2\cdot (1)}[/tex]
[tex]x = 10 \pm 2\sqrt{17}[/tex]
By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.
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