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  • If the zeroes of the quadratic polynomial x^2 + (a + 1) x + b are 2 and –3, then

If the zeroes of the quadratic polynomial x^2 + (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

Answers (1)

Answer. [D]

Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.

If 2 and –3 are the zero of p(x) = x^2 + (a + 1)x + b  then p(2) = p(–3) = 0.

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

0 = 4 + 2a + 2 + b

0 = 6 + 2a + b

2a + b = -6                        ….(1)

p(-3) = (-3)^2 + (a + 1) (-3) + b

0 = 9 - 3a - 3 + b

3a - b = 6                              ….(2)

Add equation (1) and (2)

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

2a + 3a = 0

5a = 0

a = 0

put a = 0 in (1)

2(0) + b = –6

b = –6

Hence a = 0, b = –6.

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