Question

find the zeros of polynomial P(X)=x2+2x-8​

Answer 1

Step-by-step explanation:

Given -

• p(x) = x² + 2x - 8

To Find -

• Zeroes of the polynomial

Method 1 :-

By middle term splitt -

» x² + 2x - 8

» x² - 2x + 4x - 8

» x(x - 2) + 4(x - 2)

» (x + 4)(x - 2)

Zeroes are -

x + 4 = 0 and x - 2 = 0

• x = -4 and x = 2

Method 2 :-

Using Quadratic formula :-

• x = -b ± √b² - 4ac/2a

here,

a = 1

b = 2

c = -8

Then,

x = -(2) ± √(2)² - 4×1×-8/2(1)

» -2 ± √4 + 32/2

» -2 ± √36/2

» -2 ± 6/2

Zeroes are -

x = -2 + 6/2

» 4/2

• » 2

And

x = -2 - 6/2

» -8/2

• » -4

Answer 2

ANSWER:

Given

• p( x ) = x² + 2x - 8

We can solve this by two methods

Method 1: Using factorisation

Method 2: Using quadratic equation formula

METHOD 1:

Using factorisation

x² + 2x - 8 = 0

Splitting the middle term

⟼ x² + 4x - 2x - 8 = 0

Taking common

⟼ x(x + 4) - 2(x + 4) = 0

⟼ (x + 4)(x - 2) = 0

x + 4 = 0

x = - 4

x - 2 = 0

x = 2

Hence, x = -4 , 2

METHOD 2:

Using quadratic equation formula

x = - b ± √b² - 4ac/2a

Here,

a = 1 , b = 2 , c = - 8

⤇ x = - 2 ±√2² - 4(1)(-8)/2(1)

⤇ x = -2 ± √4 + 32/2

⤇ x = - 2 ± √36/2

⤇ x = - 2 + 6/2 (or) - 2 - 6/2

⤇ x = 4/2 (or) -8/2

⤇ x = 2 or - 4

Hence, x = -4 or 2