The number of polynomials having zeroes -2 and 5 is:a)1b)3c)2d)more than 3Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Since the question doesn’t say that there are only 2 zeros of the polynomial we , there can be n number of polynomials which have two of its zeros as -2 and 5 .So the correct answer is more than 3.

Answer

These are some polynomials having common zeros -2 and 5...............................................
(x+2)(x-5), (x+2)(x-5)(x-6),
(x+2)(x-5)(x-7), (x+2)(x-5)(x-8), (x+2)(x-5)(x-9), etc.

Answer

B

Answer

We have studied that the number of degree of the polynomial same number of zeroes will just like quadratic polynomial will have 2 and cubic will have 3 zeroes .

Answer

Explanation:
To find the number of polynomials with zeroes -2 and 5, we need to consider the factors of each zero.

Factor Theorem:
The factor theorem states that if a polynomial P(x) has a factor (x-a), then the value a is a zero of P(x).

Polynomials with Zeroes -2 and 5:
Let's consider the polynomials with zeroes -2 and 5.

First Polynomial:
If the first polynomial has zeroes -2 and 5, then it must have factors (x+2) and (x-5). Therefore, the first polynomial can be written as:
P1(x) = (x+2)(x-5)

Second Polynomial:
If the second polynomial has zeroes -2 and 5, then it must also have factors (x+2) and (x-5). However, we can also introduce any additional factor, such as (x-2), to create a different polynomial. Therefore, the second polynomial can be written as:
P2(x) = (x+2)(x-5)(x-2)

Third Polynomial:
Similarly, if the third polynomial has zeroes -2 and 5, it must have factors (x+2) and (x-5). We can introduce another additional factor, such as (x+1), to create a different polynomial. Therefore, the third polynomial can be written as:
P3(x) = (x+2)(x-5)(x+1)

Additional Polynomials:
We can continue introducing additional factors, such as (x+3), (x-1), (x-3), etc., to create more polynomials with zeroes -2 and 5. Since there are infinite possibilities for introducing additional factors, the number of polynomials with zeroes -2 and 5 is more than 3.

Therefore, the correct answer is option 'D' (more than 3).

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