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form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c
? Related: Zeroes of a Quadratic Polynomial
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form a quadratic polynomial whose Ze roes are square of the zeroes ax2...
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form a quadratic polynomial whose Ze roes are square of the zeroes ax2...
Forming a Quadratic Polynomial with Squares of Zeroes
Introduction:
To form a quadratic polynomial whose zeroes are the squares of the zeroes of another quadratic polynomial, we need to understand the relationship between the roots of a polynomial and the coefficients of the polynomial.
Key Points:
- The sum of the roots of a quadratic polynomial ax^2 + bx + c is -b/a.
- The product of the roots of a quadratic polynomial ax^2 + bx + c is c/a.
Steps to Form the Polynomial:
1. Let the zeroes of the original quadratic polynomial be p and q.
2. The sum of the zeroes, p + q, is -b/a.
3. The product of the zeroes, pq, is c/a.
4. The zeroes of the new polynomial will be p^2 and q^2.
5. The sum of the new zeroes, p^2 + q^2, can be expressed in terms of p + q and pq using the identity (p + q)^2 = p^2 + q^2 + 2pq.
6. Substitute the values of p + q and pq from the original polynomial to express p^2 + q^2 in terms of a, b, and c.
7. Form the new quadratic polynomial with zeroes p^2 and q^2 as ax^2 + bx + c.
By following these steps, you can form a quadratic polynomial whose zeroes are the squares of the zeroes of another quadratic polynomial.
Introduction:
To form a quadratic polynomial whose zeroes are the squares of the zeroes of another quadratic polynomial, we need to understand the relationship between the roots of a polynomial and the coefficients of the polynomial.
Key Points:
- The sum of the roots of a quadratic polynomial ax^2 + bx + c is -b/a.
- The product of the roots of a quadratic polynomial ax^2 + bx + c is c/a.
Steps to Form the Polynomial:
1. Let the zeroes of the original quadratic polynomial be p and q.
2. The sum of the zeroes, p + q, is -b/a.
3. The product of the zeroes, pq, is c/a.
4. The zeroes of the new polynomial will be p^2 and q^2.
5. The sum of the new zeroes, p^2 + q^2, can be expressed in terms of p + q and pq using the identity (p + q)^2 = p^2 + q^2 + 2pq.
6. Substitute the values of p + q and pq from the original polynomial to express p^2 + q^2 in terms of a, b, and c.
7. Form the new quadratic polynomial with zeroes p^2 and q^2 as ax^2 + bx + c.
By following these steps, you can form a quadratic polynomial whose zeroes are the squares of the zeroes of another quadratic polynomial.
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form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial?
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form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial?.
form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for form a quadratic polynomial whose Ze roes are square of the zeroes ax2+ bx + c Related: Zeroes of a Quadratic Polynomial?.
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