Question

Find the quadratic polynomial each with the given numbers as the sun and product of its zeroes respectively.
1. 1\4,-1
2. √2,1\3
3. 0,√5

Answer 1

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

Solution :-

We know that,

$\large{\boxed{\blue{\sf{Quadratic\: polynomial = x^2 - (sum) x + product}}}}$

Put Values in all the cases

Case 1 :-

$\sf{ \implies {x}^{2} - (sum)x + product } \\ \\ \sf{ \implies {x}^{2} - \frac{1}{4}x - 1 }$

$\rule{200}{2}$

Case 2 :-

$\sf{ \implies {x}^{2} - (sum)x + product } \\ \\ \sf{ \implies {x}^{2} - \sqrt{2} x + \frac{1}{3} }$

$\rule{200}{2}$

Case 3 :-

$\sf{ \implies {x}^{2} - (sum)x + product } \\ \\ \sf{ \implies {x}^{2} - x +\sqrt 5 }$