Question

If ∝ and U are zero’s of the quadratic polynomial p(x) = 2x2− 5x + 7 find a
polynomial whose zeros ae 2∝ +3 U and 3∝ + 2 U

Answer 1

Answer:

2x²-25x+82 is the required polynomial

Step-by-step explanation:

Let the zeros of given polynomial be @ and ß

p(x)=2x²-5x+7

Here,we obtain:

@+ß=5/2 and @ß=7/2

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

Given that 2@+3ß and 3@+2ß are the zeros.

Now,

S=(2@+3ß)+(3@+2ß)

=5@+5ß

=5(@+ß)

=5×5/2

=25/2

P=(2@+3ß)(3@+2ß)

=6@²+4@ß+9@ß+6ß²

=6@²+13@ß+6ß²

=(6@²+12@ß+6ß²)+@ß

=6(@²+2@ß+ß²)+@ß

=6(@+ß)²+@ß

=6×(5/2)²+7/2

=6×25/4+7/2

=150/4+7/2

=(150+14)/4

=164/4

=82/2

➡️Required polynomial:

x²-Sx+P

=x²-25/2x+82/2

Multiplying the whole equation by 2

=2x²-25x+82