Formation of Polynomials - Class 10 Math || #Pioneer || LIVE || Misbah || Infinity Learn Class 9&10 | Summary and Q&A

TL;DR

Learn how to form polynomials when given the sum and product of zeros, focusing on quadratic polynomials.

Key Insights

• 0️⃣ Vieta's formula provides a relationship between the zeros and coefficients of a polynomial.
• 0️⃣ The discriminant of a quadratic polynomial determines if it has real zeros.
• 0️⃣ There are infinite polynomials with the same zeros, but with different coefficients.

Transcript

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Questions & Answers

Q: How can you find the value of a polynomial when the sum and product of zeros are given?

To find the value, you need to use Vieta's formula, where the sum of zeros is equal to -B/A and the product of zeros is equal to C/A.

Q: Can you find the zeros of a polynomial with a negative discriminant?

If the discriminant of a quadratic polynomial is negative, it means that the polynomial doesn't have any real zeros. However, you can still find the zeros in terms of Alpha and Beta using Vieta's formula.

Q: Are there multiple quadratic polynomials with the same zeros?

Yes, there are infinite quadratic polynomials with the same zeros. This is because you can multiply the polynomial by any non-zero real number to get different expressions while maintaining the same zeros.

Q: How can you find a polynomial when the zeros are given as fractions?

To find a polynomial with zeros as fractions, you can use the same method as before and substitute the fractions for the values of Alpha and Beta.

Summary & Key Takeaways

• The content discusses the formation of polynomials when the sum and product of zeros are given.

• It explains the relationship between the zeros and coefficients of polynomials using Vieta's formula.

• The video demonstrates the process of finding the value of a polynomial with given zeros and provides examples for better understanding.