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Question

Find a quadratic polynomial whose zeroes are:

2,3


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Solution

Zeroes of a polynomial:

The zeros of a polynomial f(x) are all the values of x that make the polynomial equal to zero.

Example:

Let, f(x)=3x2-2x-1

At, x=1,

f(1)=3×12-2×1-1=3-2-1=0

Then, 1 is a zero of f(x).

Formula:

We know that a quadratic polynomial whose zeroes are given can be represented as:

x2-(sumoftheroots)x+(productoftheroots)

Explanation:

As the zeros are given 2,3

Therefore, the product of the roots 2×3=6

The sum of the roots (2+3)

Calculation:

The required polynomial is x2-(2+3)x+6

Conclusion:

Polynomial:

A polynomial is an expression of more than two algebraic terms, including the sum of several terms that contain different powers of the same variable(s).

Here, the polynomial is k(x2-(2+3)x+6),where k is non-zero constant.

Final Answer:


Hence the polynomial is k(x2-(2+3)x+6)


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