Question

Find a quadratic polynomial, the sum and product of whose zero are
$\sqrt{2}$
and
$\frac{ - 3}{2}$

respectively. Also find its zero.​

Answer 1

As we know that,

alpha+ beta= -b/c

alpha+ beta= √2/1 (1)

Now,

alpha×beta= c/a

alpha×beta= -3/2. (2)

From (1)and (2),

a=2

b=-2√2

c= -3

So, the required polynomial= ax^2+bx+c

= 2x^2-2√2x-3