Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
√2;1÷3​

Answer 1

$3x^{2}-3\sqrt{2}x+1=0$

Step-by-step explanation:

$ax^{2}+bx+c=0$           general quadratic equation

$\alpha +\beta =-b/a$               sum of roots

$\alpha \times \beta =c/a$                  product of roots

$\sqrt{2}=-b/a$ $=\alpha +\beta$      sum of roots given

$1/3=c/a$  $=\alpha \times \beta$        product of roots given

$x^{2}+bx/a+c/a=0$

$x^{2}+\left ( -\sqrt{2} \right )x+1/3=0$

$3x^{2}-3\sqrt{2}x+1=0$      required quadratic equation