Question

a quadratic polynomial,the sum and product of whose zeroes are -4 and -1 respectively,can be?

Answer 1

A quadratic polynomial is of the form
${x}^{2} - sx + p$
Where s is the sum of roots, and P is the product of the roots of the polynomials.
Therefore, the required polynomial is
${x }^{2} - ( - 4)x + ( - 1) \\ {x}^{2} + 4x - 1$
Now you can multiply this whole polynomial by any integer, but the sum and product of the roots will be the same.

Answer 2

let p and q be the zeroes of the quadratic polynomial.

here sum of zeroes=(p+q)= -4
product of zeroes =(p*q)= -1

then general equation of polynomial if its zeroes are given is:
x^2 -(p+q)x +(p*q)

putting values of (p+q) and (p*q) in above equation we get

x^2 -(-4)x +(-1)=0
x^2 + 4x -1 =0


hence option 3 is correct.