Question

A polynomial 4x^2+12x+9 has zeros as alpha, beta. Now form a quadratic polynomial whose zeros are alpha-1, beta-1

Answer 1

4x^2 + 12x +9 = (2x+3)^2

take alpha , beta are roots

to find the equation with alpha -1 ,beta-1

put x +1 for x

(2(x +1) +3)^2

(2x +2+3)^2

(2x+ 5 )^2

4x^2 +20x +25

Answer 2

Answer:

The quadratic equation formed is $4x^{2}+ 20x+25=0$

Step-by-step explanation:

The given polynomial is $4x^{2} +12x+9=0$

It can also be written as

$4x^{2} +12x+9=(2x+3)^{2}$

Since the given roots are $-1,-1$.

We can put $x=x+1$

The required polynomial becomes $(2(x+1)+3)^{2} =0$

$(2x+2+3)^{2} =0$

$(2x+5)^{2} =0$

Expanding it, we get

$4x^{2}+ 20x+25=0$

#SPJ2