Question

Hey challenge for all the experts and genius. solve this sum. don't spam otherwise you will be known as looser

if alpha and beta are the zeros of quadratic polynomial f x is equal to 3 x square - 7 x minus 6 find a polynomial whose zeros are Alpha square and beta square
​

Answer 1

Solution:

Let p(x) represent the given polynomial

Consider @ and ß to be the zeros of the polynomial

We have,

p(x)=3x²-7x-6

Here,

•Sum of zeros: - x coefficient/x²coefficient

→@+ß= -(-7)/3

→@+ß=7/3

•Product of zeros: constant term/x²coefficient

→@ß= -6/3

We have to the values of sum of the squares of the zeros,

@²+ß²

Now,

Let S and P be the sum and product of zeros of required polynomial

★Sum of zeros of required polynomial,

S=@²+ß²

Adding and subtracting 2@ß

=@²+ß²+2@ß-2@ß

=(@²+2@ß+ß²)-2@ß

=(@+ß)²-2@ß

=(7/3)²-2(-6/3)

=49/9+12/3

=49/9+48/9

=97/7

★Product of zeros of required polynomial,

P=@²ß²

=(@ß)²

=(-6/3)²

= -2²

=4

|Required Polynomial|

x²-Sx+P

=x²-97/7x+4

Multiplying by 7,

=7x²-97x+28

P.S. I have used @ and ß instead of alpha and beta respectively

Answer 2

Answer:

3x^2-7x-6

3x^2-9x+2x-6 middle term split

3x(x-3)+2(×-3)

3x+2=0 x=-2/3 =alfa

x-3=0 x=3=beta

Step-by-step explanation:

alpha^2=(-2/3)^2=4/9

beta^2=3^2=9

so the polynomial be

alpha+beta=-b/a=4/9+9

=85/9

alpha×beta=c/a=4/9×9=4

so polynomial be

9x^2-85x+36

to verify

9x^2-85x+36

9x^2-81x-4x+36 middle term split

9x(x-9)-4(x-9)

9x-4=0 x=4/9***

x-9=0 x=9***

***as we get above

verified