Question
Write a quadratic polynomial, sum of whose zeros is $2\sqrt{3}$ and their product is $2.$
✓
Answer
As we know that the quadratic
polynomial $f(x) = k[x^2 - $(sum of their roots)x + (product of their roots)]
According to question,
(sum of their roots) $=2\sqrt{3}$
And (product of their roots) = 2
Thus Putting the value in above,
$\text{f}(\text{x})=\text{k}\big[\text{x}^2-2\sqrt{3}\text{x}+2\big]$ where k is real number.
Therefore, the quadratic polynomial be
$\text{f}(\text{x})=\text{k}\big[\text{x}^2-2\sqrt{3}\text{x}+2\big]$
polynomial $f(x) = k[x^2 - $(sum of their roots)x + (product of their roots)]
According to question,
(sum of their roots) $=2\sqrt{3}$
And (product of their roots) = 2
Thus Putting the value in above,
$\text{f}(\text{x})=\text{k}\big[\text{x}^2-2\sqrt{3}\text{x}+2\big]$ where k is real number.
Therefore, the quadratic polynomial be
$\text{f}(\text{x})=\text{k}\big[\text{x}^2-2\sqrt{3}\text{x}+2\big]$
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