Question

the numbers of polynomial having zeros -3 and 7. ​

Answer 1

Answer:

Infinite

Step-by-step explanation:

Let us first find one polynomial, p(x) with these 2 zeroes.

if -3 is a zero, then x = -3.

Then (x+3) is a factor of p(x)

if 7 is a zero, then (x-7) is a factor of p(x)

p(x) = (x+3)(x-7)

= x² -7x + 3x -21

= x² - 4x - 21

so, p(x) = x² - 4x - 21 is one polynomial whose zeroes are -3 and 7.

If we multiply or divide this polynomial by a constant, then the zeroes will remain same.

for example,

p(x) = 2(x²-4x-21)

= 2 (x+3)(x-7)

= 2x+6 × (x-7) or  (x+3) × 2x-14

for 2x+6, x = -6/2= -3

for 2x-14, x= 14/2 = 7

∴the zeroes remains the same.

like this we can multiply or divide p(x) by infinite number of constants.

therefore, the number of polynomials having zeroes -3 and 7 are infinte.