Question

IF THE ZEROES OF THE QUADRATIC POLYNOMIAL X2+(A+B)X+B ARE 2 ND -3 THE THA VALVUE IS

Answer 1

Answer:

6

Step-by-step 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

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

hope it was helpful : )