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Find the zeroes of the polynomial $x 2 + 16 x − 2$ .

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An Intiative by Sri Chaitanya

43, − 32

− 43, − 32

34, − 23

− 34, − 23

answer is A.

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Detailed Solution

Given polynomial is

x 2 + 16 x − 2

. We need to find the zeroes of the given polynomial.
Zeroes of the polynomials are those where

p (x) = 0

.
In splitting the middle term method we split the middle term of quadratic equation in

a

and

b

such that,

a + b =

middle term

a × b =

product of first and third term
Let us assume that

p (x) = x 2 + 16 x − 2.

⇒ p (x) = 6 x 2 + x − 12 6

Equating

p (x)

0

we have,

6 x 2 + x − 12 = 0 ... (i)

Using, splitting the middle term approach, in equation

(i)

, we have,

a = 9 x & b = − 8 x

Therefore, we have,

6 x 2 + x − 12 = 0 ⇒ 6 x 2 + 9 x − 8 x − 12 = 0 ⇒ 3 x (2 x + 3) − 4 (2 x + 3) = 0 ⇒ 3 x − 4 2 x + 3 = 0 ∴ x = 43, − 32

The zeroes of polynomial

x 2 + 16 x − 2

are

43

and

− 3 2

.
Therefore, option 1 is correct.

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