Question

If α and β are zeroes of the polynomial 6X2 – 7X -3, then form a quadratic polynomial whose zeroes are 2α and 2β

Answer 1

6x^2-9x+2x-3=0
3x(2x-3)+(2x-3)=0
(2x-3)(3x+1)=0
x=3/2&-1/3
$\alpha = 3 \div 2and \: \beta = - 1 \div 3$
So
$2 \alpha = 3 \: \: and \: \: \: 2 \beta = - 2 \div 3$
Sum of zeroes =3+(-2/3)=7/3
Product of zeroes =3(-2/3)=-2
Reqd eqn is
x^2 - 7x/3-2=0
3x^2-7x-6=0

Answer 2

Answer:

aloha user

Step-by-step explanation:

6x^2-9x+2x-3=0

3x(2x-3)+(2x-3)=0

(2x-3)(3x+1)=0

x=3/2&-1/3

\alpha  = 3 \div 2and \:  \beta  =  - 1 \div 3

So

2 \alpha  = 3 \:  \: and   \:  \:  \: 2 \beta  =  - 2 \div 3

Sum of zeroes =3+(-2/3)=7/3

Product of zeroes =3(-2/3)=-2

Reqd eqn is

x^2 - 7x/3-2=0

3x^2-7x-6=0

hope it helps