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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