If α and β are the zeroes of the polynomial x2-4x+3, then form a quadratic polynomial whose zeroes are 3α and 3β.

Question : If α and β are the zeroes of the polynomial x²-4x+3, then form a quadratic polynomial whose zeroes are 3α and 3β.

Doubt by Charu

Solution : 

p(x)=x²-4x+3
a=1

b=-4

c=3

Sum of Zeroes

α+β = -b/a

α+β = -(-4)/1

α+β = 4

Product of Zeroes

αβ = c/a

αβ = 3/1

αβ = 3

For New Polynomial 

Sum of Zeroes (S) 
S= 3α+3β
S= 3(α+β)
S= 3(4)
S=12

Product of Zeroes (P)
P= (3α)(3β)
P= 9(αβ)
P=9(3)
P=27

New Polynomial will be given by 

p'(x)=x²-Sx+P
p'(x)=x²-(12)x+27
p'(x)=x²-12x+27

which is the required polynomial.