Find the equation of the circle whose diameter is the chord x + y = 3 of the circle x2 + y2 - 2x - 3 = 0
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Given:
The given quadratic polynomial is :
To find:
The quadratic polynomial whose zeroes are negatives of the zeroes of the given polynomial.
Solution:
We have,
Equate the polynomial with 0 to find the zeroes.
Splitting the middle term, we get
The zeroes of the given polynomial are -3 and 4.
The zeroes of a quadratic polynomial are negatives of the zeroes of the given polynomial. So, the zeroes of the required polynomial are 3 and -4.
A quadratic polynomial is defined as:
Therefore, the required polynomial is .