Find Quadratic Polynomial from Sum and Product of Zeroes

 

❓ Question

Find a quadratic polynomial, the sum and product of whose zeroes are:

$$-3 \text{ and } 2$$

respectively.

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🖼️ Solution Image

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✍️ Short Explanation

For a quadratic polynomial, if:

• Sum of zeroes $=S$
  
• Product of zeroes $=P$
  

then the polynomial is:

$$f(x)=x^2-Sx+P$$

💯

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🔹 Step 1 — Write Given Values

Sum of zeroes:

$$S=-3$$

Product of zeroes:

$$P=2$$

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🔹 Step 2 — Use Standard Formula

$$f(x)=x^2-Sx+P$$

Substitute the values:

$$f(x)=x^2-(-3)x+2$$

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🔹 Step 3 — Simplify

$$f(x)=x^2+3x+2$$

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✅ Final Answer

Required quadratic polynomial is:

$$\boxed{x^2+3x+2}$$

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⭐ Key Insight

If:

• Sum of zeroes $=S$
  
• Product of zeroes $=P$
  

then:

$$\boxed{x^2-Sx+P}$$

gives the required quadratic polynomial.

🧠 Memory Line:

Sum ka sign opposite hota hai, product same rehta hai

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📚 Related Topics

• Zeroes of Polynomial Using Graph Concept Explained
• Zeroes and Coefficients of Quadratic Polynomial
• Prove that Given Numbers are Irrational