P3 POLYNOMIALS Chapter-2 Exercise 2.2 | Class 10th Mathematics | Relp betw Zeroes and Coef of a Poly

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x^2 – 2x – 8
solution :
x^2 - 2x - 8
Step 1: Find the Zeroes of the Polynomial
We factor the polynomial:
x^2 - 2x - 8 = (x - 4)(x + 2)
So, the zeroes are:
x=4 and x = -2

Step 2: Verify the Relationship between Zeroes and Coefficients
Standard form of a quadratic polynomial:
ax^2 + bx + c
Here:
• a = 1
• b = -2
• c = -8
Let the zeroes be α=4\alpha = 4, β=−2\beta = -2
Sum of zeroes:
α+β=4+(−2)=2
Compare with −b/a=−(−2)/1=2
Verified.

Product of zeroes:
α⋅β=4⋅(−2)=−8
Verified.
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📌 Final Answer:
• Zeroes: 4 and -2
• Relationship Verified:
o Sum = −b/a
o Product = c/a


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