Write a quadratic polynomial, sum of whose zeros is 23 and their … - Vidyadip

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
$\text{f}(\text{x})=\text{k}\big[\text{x}^2-2\sqrt{3}\text{x}+2\big]$

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