Question

if alpha and beta are the roots of the polynomial f(x) = x^2-3x+k such that alpha -beta =1 find the value of k ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Hey

f(x)=x^2-3x+k

Given that @ and ß are the zeros of the polynomial and @-ß=1.............(2)

Now,

@+ß= -(3)=3...................(1)

@ß=k...................(3)

We find,

@^2 + ß^2=(@+ß)^2- 2@ß=(3)^2-2k=9-2k.......................(4)

Thus,

Squaring (2),

(@-ß)^2=(1)^2

=>@^2+ß^2-2@ß=1

=>9-2k-2k=1 [Using (3) and (4)]

=> -4k= -8

=>k=2

I used @ and ß instead of alpha and beta respectively.

I hope it helps you.

It can also be solved by adding(1) and (2). Hence, finding individual values of @ and ß.Then multiplying them which is equal to k.