Question

if 2 and -3 are the zeroes of quadratic polynomialx2 +(a+1)x+b, then find the value of a and b​

Answer 1

Answer:

• a = 0
• b = -6

Explanation:

Given polynomial,

⇒ x² + (a + 1)x + b

On comapring with the general form of a quadratic equation ax² + bx + c

• a = 1
• b = (a + 1)
• c = b

Then,

Sum of zeros = -b/a = -(a + 1)/1 = - a - 1 . . . . .(i)

Product of the zeros = c/a = b . . . . . (ii)

Here, the zeros of the polynomial given is 2 and -3

Then,

Sum of the zeros = 2 + (-3)

From (i) :-

⇒ 2 + (-3) = - a - 1

⇒ 2 - 3 = - a - 1

⇒ -1 = - a - 1

⇒ a = 1 - 1

⇒ a = 0

∴ The value of a = 0

And also,

Product of zeros = 2 × (-3)

From (ii) :-

⇒ 2 × (-3) = b

⇒ -6 = b

∴ The value of b is -6

________________________