Question

if zeros of polynomial x square +( A + 1 )x +b are 2 and minus 3 then find the value of (a + b)

Answer 1

QuesTion

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

SoluTion

given polynomial is

x² + (a + 1) x + b

given zeroes of polynomial are

2  and  - 3

so,

$\bf{sum\:of\:zeroes=\frac{-(coefficient\:of\:x)}{coefficient\:of\:x^2}}$

2 + (- 3 ) = - (a + 1) / 1

- 1 = - a - 1

so,

$\boxed{\red{\bf{a=0}}}$

now,

$\bf{ product \:of\:zeroes=\frac{constant\:term}{coefficient\:of\:x^2}}$

2 * - 3 = b / 1

so,

$\boxed{\red{\bf{b=-6}}}$

therefore,

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

so,

$\boxed{\red{\bf{a+b=-6}}}$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

P(x) = x² + (a + 1)x + b

Given, P(2) = 0 and P(- 3) = 0

Putting, P(2), we get

⇒ (2)² + (a + 1)(2) + b = 0

⇒ 4 + 2a + 2 + b = 0

⇒ 6 + 2a + b = 0

⇒ 2a + b = - 6 ... (i)

Putting, P(- 3), we get

⇒ (- 3)² + (a + 1)( - 3) + b = 0

⇒ 9 - 3a - 3 + b = 0

⇒ 6 - 3a + b = 0

⇒ - 3a + b = -6 ..... (ii)

Subtracting Eq (i) and (ii), we get

⇒ 2a + b - (- 3a + b) = - 6 - (- 6)

⇒  2a + b + 3a - b = - 6 + 6

⇒  5a = 0

⇒  a = 0

Putting a's value in Eq (i), we get

⇒ 2a + b = - 6

⇒ 2(0) + b = - 6

⇒ b = - 6

We have to find a + b

⇒ a + b = 0 + (- 6) = - 6

Hence, the value a + b is - 6.