Question

If alpha and beta are zeroes of the polynomial x2-4x+3, then find the quadratic polynomial whose roots are 3alpha and 3beta

Answer 1

here is the answer

hope you undersrands it

Answer 2

Answer:

Required quadratic polynomial is $x^2-12x+27=0$    

Step-by-step explanation:

Given : If alpha and beta are zeroes of the polynomial $x^2-4x+3$.

To find : The quadratic polynomial whose roots are $3\alpha$ and $3\beta$

Solution :

If alpha and beta are zeroes of the polynomial $x^2-4x+3$.

Then, $\alpha+\beta=-\frac{b}{a}=-\frac{-4}{1}$

$\alpha+\beta=4$ ....(1)

$\alpha\times\beta=\frac{c}{a}=\frac{3}{1}$

$\alpha\beta=3$ ....(2)

Now, The new quadratic polynomial has roots $3\alpha$ and $3\beta$

So, Sum of roots is

$3\alpha+3\beta=3(\alpha+\beta)=3\times 4=12$

Product of roots is

$3\alpha\times 3\beta=9(\alpha\times\beta)=9\times 3=27$

The required polynomial is

$x^2-(3\alpha+3\beta)x+(3\alpha3\beta)$

Substitute the values,

$x^2-(12)x+(27)=0$

Therefore, Required quadratic polynomial is $x^2-12x+27=0$