Find a quadratic polynomial, the sum of whose zeroes is 5 and their product is 6. Hence, find zeroes of the polynomial.

Answer

N/a

Explanation

Let `alpha` and `beta` be the zeroes of the polynomial p(x).
Given that `alpah+beta`=5 and `alphabeta`=6
Now, `" " p(x)=x^(2)-(alpha+beta)x+alpha beta=x^(2)-5x+6=x^(2)-3x-2x+6`
`=x(x-3)-2(x-3)=(x-3)=(x-3)(x-2)` ,brgt There may be so many different polynomials which satisfy the given condition. Actually the general quadratic polynomial will be `k(x^(2)-5x+6)`, where `k ne 0`
`:. " "` p(x)=0
`implies " " (x-2)(x-3)=0`
`implies " " (x-2)=0" " or " "(x-3)=0`
`implies " " 2=2 " " or " " x=3`
`:.` Zeroes are 2 and 3. `" " ` Ans.
Note : If is asked that find a polynomial, then find only one quadratic polynomial i.e., without k, otherwise, in general you should write k in the multiplication.