Question

Find a quaragratic polynomial whose sum and productof zeroes are√2 and 3 respectively

Answer 1

Hello friends!!

Here is ur answer :

Let x and y are the zeroes of the equation.

( a - x) ( a - y)

Using identity, ( a + b) ( a + c) = a² + ( b + c) a+ bc

${a}^{2} + ( - x - y)a + ( - x)( - y)$


${a}^{2} - (x + y)a + xy$


${a}^{2} - (sum \: \: of \: \: zeroes) + (product \: \: of \: \: zeroes)$



Now come to the question,

Sum of the zeroes
$\sqrt{2}$



Product of the zeroes
$3$


The quadratic equation will be

${x}^{2} - \sqrt{2}x \: + 3$


HOPE IT HELPS YOU ...

Answer 2

We know that, The General form of a quadratic polynomial whose Sum of roots and products of roots is given :

x² - ( Sum of roots) x + ( Product of roots )

In the above question,
Sum of roots = √2
Product of roots = 3 .

Now, The quadratic polynomial is x² - √2x + 3 .

Hope helped!