Question

if αβ are zeros of x2 - 4x - 3, find a quadratic polynomial whose zeros are 3α and 3β.​

Answer 1

Answer:

Step-by-step explanation:

Given  α and β are zeroes of the polynomial  f(x)  = x^2 - 4x - 3

Comparing it with ax^2 + bx + c

a= 1       b =  -4      &  c  = -3

α + β = (  -b / a  )   =  - ( - 4 ) / 1 = 4

αβ =  c / a  =  -3  / 1 =  -3

So quadratic polynomial whose zeros are 3α and 3β is

​( 3α + 3β ) = 3  ​( α + β ) = 3 x 4 = 12

3α x 3β = 3( α β) = 3 x ( -3 )   =  -9

If 3α, 3β are zeros of the quadratic polynomial then the equation is

x^2 - (3α + 3β) x + 9αβ

then

x^2 - 12x  - 9 .