If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then
a. a = -7, b = -1
b. a = 5, b = -1
c. a = 2, b = -6
d. a = 0, b = -6

Solution:

Given, the quadratic polynomial is x² + (a + 1)x + b.

The zeros of the polynomial are 2 and -3.

We have to find the value of a and b.

We know that, if 𝛼 and ꞵ are the zeroes of a polynomial ax² + bx + c, then

Sum of the roots is 𝛼 + ꞵ = -b/a

Product of the roots is 𝛼ꞵ = c/a

Here, 𝛼 = 2 and ꞵ = -3

Coefficient b = (a + 1)

Coefficient a = 1

Coefficient c = b

Sum of the roots = -b/a = -(a+1)/1 = -1 - a

𝛼 + ꞵ = 2 - 3 = -1

So, -1 = -1 - a

-1 + a = -1

a = -1 + 1

a = 0

Product of the roots = c/a = b/(a+1)

= b/(0+1)

= b

𝛼ꞵ = (2)(-3) = -6

So, b = -6

Therefore, the values of a and b are 0 and -6.

Try this: If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 3

If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then a = -7, b = -1, a = 5, b = -1, a = 2, b = -6, a = 0, b = -6

Summary:

If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then a = 0 and b = -6

☛ Related Questions: