Question

1If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial. ​

Answer 1

Step-by-step explanation:

α + β = -6 and αβ = 5,

x²-(-6)x+5

x²+6x+5

Answer 2

Step-by-step explanation:

Given:

If α and β are the zeros of the polynomial f(x) = x2 + px + q, To find: A polynomial having 1 α 1α and 1 β 1β is its zeros is Solution: f(x) = x2 + px + q

We know, Since α, β are zeroes of given polynomial, ⇒ α + β = – p and αβ = q Let S and P denote respectively the sum

=The product of zeroes of the required polynomial, So, Put the values of α + β and αβ in (1) and (2) to get, ⇒ S = − p q −pq

= P = 1 q 1q We know equation having 2 zeroes is of form,k (x2 - (sum of zeroes) x + product of zeroes)

= For a polynomial having 1 α 1α and 1 β 1βis its zeros the equation becomes, x2 + p/q x + 1/q

= 0 So here we get, g(x) = qx2 + px + 1..

Hope its help..