Question

If alpha and beta are the zeros of polynomial x^2-4x+3 form a quadratic polynomial whose zeroes are 3alpha and 3beta

Answer 1

 x2-5x+k

Here, a=1, b=-5 and c=k

Now, alpha+beta= -b/a= -(-5)/1= 5

alpha*beta= c/a= k/1= k

Now, apha-beta=1

Squaring both sides, we get,

(alpha-beta)2=12

=> (alpha+beta)2-4*aplha*beta=1

=> (5)2-4k=1

=> -4k= 1-25

=> -4k= -24

=> k=6

So the value of k is 6.

Hope it helps!!