3. If p, q are the zeroes of quadratic polynomial then the quadratic polynomial is

If \( p \) and \( q \) are the zeroes of a quadratic polynomial, then the quadratic polynomial can be expressed in the form:

\[
f(x) = a(x - p)(x - q)
\]

where \( a \) is a constant (the leading coefficient).

Expanding this expression, we get:

\[
f(x) = a(x^2 - (p + q)x + pq)
\]

So, the quadratic polynomial with zeroes \( p \) and \( q \) is:

\[
f(x) = ax^2 - a(p + q)x + apq
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the zeroes of a quadratic polynomial?
2. What is the sum and product of the zeroes in a quadratic equation?
3. How does the value of \( a \) affect the graph of the quadratic polynomial?
4. What are the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \)?
5. How can you factor a quadratic polynomial if the zeroes are known?

**Tip:** To quickly find the sum and product of the roots of a quadratic equation \( ax^2 + bx + c = 0 \), use the formulas: sum = \(-\frac{b}{a}\) and product = \(\frac{c}{a}\).

If p, q are the zeroes of quadratic polynomial then the quadratic polynomial is

Learn how to find the quadratic polynomial with zeroes p and q using the formula f(x) = a(x - p)(x - q). This problem covers key concepts in quadratic equations and polynomials. Suitable for students in Grades 9-12.

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