Q. 3 F5.0( 3 Votes )

# Let us check the following statements—

The two zeros of the polynomial P(x) = x^{2} – 2x – 8 are 4 and (–2).

Answer :

Formula used/Theory.

There is some value of ‘x’ for which the P(x) comes to 0, that value of ‘x’ is said to be zero of polynomial P(x)

We have,

P(x) = x^{2} – 2x – 8

And zero of the polynomial P(x) are 4 and -2

Then,

Zero of the polynomial P(x)

Means P(x) = 0

x^{2} – 2x – 8 = 0

As in quadratic eq

We have to divide (-2x) in 2 parts such that product comes to (-8x^{2})

Hence the factors are :-

(-x) × (8x) addition gives 8x – x = 7x

(-2x) × (4x) addition gives 4x – 2x = 2x

(-4x) × (2x) addition gives 2x – 4x = -2x

Hence factors are -4x and 2x

x^{2} – 4x + 2x – 8 = 0

x(x – 4)+2(x – 4) = 0

(x+2)(x – 4) = 0

x+2 = 0 and x – 4 = 0

x = (-2) and x = 4

∴ Zero of polynomial P(x) is 4 and -2

Conclusion.

Hence, the statement is True

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