Question

find a quadratic polynomial each with given numbers as the sum and product of its zeroes respectively​

Answer 1

Answer:

3x^2-3√2x+1

Step-by-step explanation:

Alpha +beta=-b/a

alpha×beta = C/a

Answer 2

ii ) sum zeroes = √2

$\frac{ - b}{a} = \frac{ \sqrt{2} }{1}$

$\frac{ b}{a} = \frac{ - \sqrt{2} \times 3}{1 \times 3}$

$\frac{ b}{a} = \frac{-3 \sqrt{2} }{3}$

product of zeroes =1/3

$\frac{c}{a} = \frac{1}{3}$

Therefore a =3 , b =- 3√2 , c = 1

Quadratic polynomial is ax²+bx+c

= 3x²- 3√2x +1

v )

sum of zeroes = - 1/4

$\frac{ - b}{a} = \frac{ - 1}{4}$

$\frac{ b}{a} = \frac{ 1}{4}$

product of zeroes = 1/4

$\frac{ c}{a} = \frac{ 1}{4}$

Therefore a =4 , b = 1 , c = 1

Quadratic polynomial is ax²+bx+c

= 4x²+1x +1

or 4x²+ x +1