If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and −3, find the values of a and b

Video Explanation

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Given

Quadratic polynomial: f(x) = x² + (a + 1)x + b

Zeroes of the polynomial are: 2 and −3

To Find

The values of a and b.

Solution

For a quadratic polynomial ax² + bx + c:

• Sum of zeroes = −(coefficient of x) / (coefficient of x²)
• Product of zeroes = constant term / coefficient of x²

Step 1: Find the Sum of Zeroes

2 + (−3) = −1

According to the polynomial:

Sum of zeroes = −(a + 1)

So,

−(a + 1) = −1

a + 1 = 1

a = 0

Step 2: Find the Product of Zeroes

2 × (−3) = −6

According to the polynomial:

Product of zeroes = b

∴ b = −6

Final Answer

a = 0 and b = −6

Correct Option

(d) a = 0, b = −6

Conclusion

Hence, if the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and −3, then a = 0 and b = −6.