Question

from a quadratic polynomial whose zeroes are -3 and -1

Answer 1

Given :-

Let, $\alpha$ = - 3 and $\beta$ = - 1

Now,

Sum of zeroes, S = $\alpha$ + $\beta$

S = - 3 + ( - 1 ) = - 3 - 1 = - 4

Product of zeroes, P = $\alpha \beta$

P = ( - 3 ) ( - 1 ) = 3

Now,

Required polynomial is -

p ( x ) = x² - ( S ) x + ( P )

p ( x ) = x² - ( - 4 ) x + ( 3 )

p ( x ) = x² + 4x + 3

Answer 2

the quadratic equation is in form of ax^2+bx+c=0
and with zeroes -3 and -1 quad.poly. will be..
k[x^2-(alpha + biita)x+alpha *biita]
k[x^2-(-3-1)x+(-3*-1])
k[x^2+4x+3]
where k is constant