Question

4. Find a quadratic polynomial, the sum and the product of whose zeroes are 3 and 2 respectively​

Answer 1

Let,

the polynomial be

$p(x)=a{x}^{2}+bx+c$

Sum of zeroes= -3

$-\frac{b}{a}=-3\\\\assuming\:a=1\\\\-\frac{b}{1}=-3\\\\-b=-3\\\\→\underline{b=3}$

Product of zeroes =2

$\frac{c}{a}=2\\\\assuming\:a=1\\\\\frac{c}{1}=2\\\\→\underline{c=2}$

Now, a = 1, b = 3,c = 2

Hence, the required quadratic polynomial

$p(x)=a{x}^{2}+bx+c\\\\=1{x}^{2}+3x+2\\\\={x}^{2}+3x+2\\\\\underline{\boxed{\sf{ {x}^{2}+3x+2}}}$

Answer 2

Step-by-step explanation:

Let 3 and 2 be the zeroes of the polynomial.

x² - (Sum of zeroes)x + product of zeroes

= x² - (3+2)x + (3)(2)

= x² - 5x + 6