wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find a quadratic polynomial whose zeroes are:

1,2


Open in App
Solution

Definition:

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)=3×12-2×1-1orf(1)=3-2-1orf(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 1,2

Therefore, the sum of the roots (1+2)
Product of the roots= 1×2=2
Calculation:

The required polynomial is

x2-(1+2)x+2

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-(1+2)x+2),where k is any non zero constant.

Final answer:

Hence the polynomial is k(x2-(1+2)x+2),where k is any non zero constant


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Heat Capacity
CHEMISTRY
Watch in App
Join BYJU'S Learning Program
CrossIcon