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To find a quadratic polynomial whose zeroes are given as 5 and 3, we can use the fact that if \( \alpha \) and \( \beta \) are the zeroes of a quadratic polynomial, then the polynomial can be written as:

\[
p(x) = a(x - \alpha)(x - \beta)
\]

Given that the zeroes are 5 and 3, the polynomial will be:

\[
p(x) = a(x - 5)(x - 3)
\]

Assuming \( a = 1 \) for simplicity, we can expand the expression:

\[
p(x) = (x - 5)(x - 3)
\]

Now, applying the distributive property:

\[
p(x) = x^2 - 3x - 5x + 15
\]

\[
p(x) = x^2 - 8x + 15
\]

Thus, the quadratic polynomial whose zeroes are 5 and 3 is:

\[
p(x) = x^2 - 8x + 15
\]

Would you like more details on this or any questions? Here are some related topics:

1. How do you find a quadratic polynomial given different types of roots?
2. How does the value of \(a\) affect the quadratic polynomial?
3. What are the properties of quadratic polynomials with real zeroes?
4. How do you solve quadratic equations using the factorization method?
5. What is the significance of the discriminant in quadratic equations?

**Tip:** The sum of the roots of a quadratic equation is equal to \(-b/a\) and the product is \(c/a\), which can help verify your equation!

Find a quadratic polynomial whose zeroes are 5 and 3.

Learn how to find a quadratic polynomial when the zeroes are given as 5 and 3. This problem explores core algebraic concepts such as the sum and product of roots, and uses the quadratic polynomial formula. Suitable for students in Grades 9-10.

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