Polynomials Question 1 || 9&10 Math Capsule || Misbah Sir || Infinity Learn Class 9&10 | Summary and Q&A

TL;DR

Given a polynomial and its zeros, find the value for a given number by using the concept of polynomial zeros.

Key Insights

• 😥 The value of a polynomial at certain points can be found by substituting those points into the polynomial representation formed by its zeros.
• 0️⃣ The concept of zeros of a polynomial helps represent the polynomial accurately and simplify calculations.
• 😥 Using the concept of polynomial zeros, finding the value of P(4) + P(0) can be done more efficiently than individually substituting each point.

Transcript

Read and summarize the transcript of this video on Glasp Reader (beta).

Questions & Answers

Q: How can you find the value of P(4) and P(0) in a given polynomial with given zeros?

To find P(4), we can substitute 4 into the polynomial representation using the zero factors. Similarly, to find P(0), we substitute 0 into the polynomial representation.

Q: Why can we assume one more zero, α, for the polynomial with given zeros?

Since the polynomial has a degree of four and three zeros are given, according to the fundamental theorem of algebra, there must be one more zero, represented by α.

Q: Why can we represent the polynomial as (x - 1)(x - 2)(x - 3)(x - α)?

Using the concept of polynomial zeros, we know that each zero corresponds to a factor in the polynomial. Therefore, by multiplying the factors corresponding to the given zeros, we can represent the polynomial accurately.

Q: How do we simplify the expression for P(4) and P(0) using the polynomial representation?

Substituting 4 into the polynomial representation gives us 24 - 6α for P(4), and substituting 0 gives us 6α for P(0). Therefore, P(4) + P(0) simplifies to 24.

Summary & Key Takeaways

• The question asks to find the value of P(4) + P(0) for a polynomial with given zeros.

• By using the concept of polynomial zeros and representing the polynomial with its factors, the question can be solved more efficiently.

• The value of P(4) is found to be 24 - 6α, and the value of P(0) is found to be 6α. Therefore, P(4) + P(0) equals 24.