Question

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

Answer 1

Answer :

a = 0

b = -6 .

Explanation :

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)

$6 + 2(0) + b = 0 \\ ⇒ b = - 6$

hopefully its helped u dear :)

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