Question

If a and Bare zeroes of the polynomial p(x)=2x2 - 5x + 7, find a polynomial whose
zeroes are 2a + 3 and 2B+ 3.
obromial whose​

Answer 1

Answer:

Given that

a and b are the zeros of

x

2

−2x+3

Then,

We know that

Sum of zeros =−

coeff. of x

2

coeff. of x

a+b=−

+1

−2

a+b=2−−−−−−−−(1)

Now,

Product of zeros =

coeff. of x

2

constant term

a.b=

1

3

ab=3−−−−−−−−−−−(2)

If 2a+3 and 2b+3 are the zeros of other polynomial.

Then

Sum of zeros =2a+3+2b+3

=2(a+b)+6

=2(2)+6

=10

Sum of zeros =10

Product of zeros =(2a+3)(2b+3)

=4ab+6a+6b+9

=4ab+6(a+b)+9

=4×3+6×2+9

=12+12+9

=24+9

Product of zeros =33

Now,

Equation of polynomial

x

2

− (Sum of zeros) x+ product of zeros =0

x

2

−10x+33=0

Hence, this is the answer.