Question

If a and Bare the zeroes of the polynomice
6y2-7y +2
find a quadratic polynomial
whose zeros are
1 and I
B В​

Answer 1

Let the roots of the given equation be 'a' &'b' .

a+b=-(-7)/6=7/6. .....(1)

ab=2/6=1/3. .....(2)

Now,the required equation has roots: 1/a & 1/b.

sum of roots,S=(1/a)+(1/b)

=(a+b)/ab

=(7/6)÷(1/3). {from 1 & 2}

S =7/2. ...(3)

product of roots,P=(1/a)×(1/b)

=1/(ab)

=1÷(1/3)

P =3. ...(4)

The required equation will be of the form:

y^2 -Sy+P = y^2-(7/2)y+3=O [from 3 & 4]

=2y^2-7y+6=0

Hence,the required equation is:

2y^2 - 7y + 6 = 0