If the zeros of the quadratic polynomial x2 + (a + 1)x + b are 2 and - 3,

Then


Zeroes of a polynomial is all the values of x at which the polynomial is equal to zero.

2 and - 3 are the zeroes of the polynomial p(x) = x2 + (a + 1)x + b


i.e. p(2) = 0 and p(- 3) = 0


p(2) = (2)2 + (a + 1)(2) + b = 0


= 4 + 2a + 2 + b = 0


= 6 + 2a + b = 0 (1)


P(- 3) = (- 3)2 + 9 + (a + 1)(- 3) + b = 0


= 9 - 3a - 3 + b = 0


= 6 - 3a + b = 0 (2)


Equating (1) = (2), as both the equations are equal to zero. Hence both equations are equal to each other.


6 + 2a + b = 6 - 3a + b


= 5a = 0


a = 0


Putting the value of ‘a’ in (1)


6 + 2(0) + b = 0


b = - 6


OR


The equation of a quadratic polynomial is given by x2 - (sum of the zeroes) x + (product of the zeroes)


Sum of the zeroes = - (coefficient of x) ÷ coefficient of x2


sum of the zeroes = - (a + 1)


= 2 - 3 = - a - 1


= - 1 + 1 = - a


= - a = 0


a = 0


Product of the zeroes = constant term ÷ coefficient of x2


b = product of the zeroes


= 2(- 3)


= 6

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