Question

if polynomial p[x] is divisible by [x-3] and 2 is a zero of p[x],write a factor of p[x] of degree 2.

Answer 1

Answer:

Required factors of p[x] are ( x - 2 ) and ( x - 3 ).

Step-by-step explanation:

It is given that the polynomial p[x] is of degree 2 and divisible by ( x - 3 ), also, one zero is 2.

Let the required equation be ( x - 3 )( x - k ) = 0 [ in factorized form, k is one another zero ]. We have taken ( x - 3 ) in the factorized form, as it is divisible by ( x - 3 ).

Value of k should be 2, since 2 is an another zero of p[x].

Thus,

= > p[x] = ( x - 3 )( x - 2 )

Hence the required factors of p[x] are ( x - 2 ) and ( x - 3 ).

And,

= > p[x] = x( x - 2 ) - 3( x - 2 )

= > p[x] = x^2 -2x - 3x + 6

= > p[x] = x^2 - 5x + 6