Question

Zeros of the polynomial x2-under root 2 x-12

Answer 1

x2-✅2x-12
x2-3✅2x+2✅2x-12
x (x-3✅2)+ 2✅2(x-3✅2)

(x-3✅2) (x+2✅2)
X-3✅2=0. , X+2✅2=0
X=3✅2. , x=-2✅2
These are two zeroes

Answer 2

Concept:

Zeroes of the polynomials are the value of the variable, which satisfies the polynomial and the value of the polynomial becomes zero as a whole. The number of zeroes of the polynomial is equal to the degree of the polynomial.

Given:

The polynomial x² -√2x-12.

Find:

The zeroes of the polynomial,

Solution:

Factorizing the polynomial using splitting the middle term,

f(x) = x² -√2x-12

f(x)= x² -(3√2-2√2)x -12

f(x) = x²-3√2x+2√2x-12

Taking the common terms out, and equating to find out the zeroes,

(x-3√2)(x+2√2) = 0

(x-3√2) = 0 , (x+2√2) = 0

x = 3√2 ,  x = -2√2

Hence, the zeroes of the given polynomial x² -√2x-12 are 3√2 and -2√2.

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