Question

verify whether tge following are zeroes ofbthe polynonial indicated against them . p (x) = x ³-3x²+4x -12 , x = 3​

Answer 1

Solution :

When we substitute the value of (x) in the polynomial by (3) we get :

$\rm{ p(x) = {x}^{3} - {3x}^{2} + 4x - 12}$

$\longrightarrow{\rm{ p(3) = {(3)}^{3} - 3 \times{(3)}^{2} + 4(3) - 12}}$

$\longrightarrow{\rm{ p(3) = 27 - 27 + 12 - 12}}$

$\implies\boxed{\rm{ p(3) = 0}}$

So , we can conclude that p(3) is a zero of the given polynomial.

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✓ Zeros of the polynomial :

The number which when substituted in the place of (x) in the given polynomial gives 0 as a remainder is called the zero of the polynomial.

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There are 3 parts in a polynomial :

1. Constant : The term that never changes.
2. Variable : The term that depends upon the operations.
3. Coefficient : The term that is either a number or a constant that is found before the variable and is multiplied to it .

eg:

$\tt{ {2x}^{2} - x + 18}$

Constant : 18

Variable : x

Coefficient : 2 (2 is coefficient of ${x}^{2})$

Answer 2

$\huge \tt \underline {Solution }$

$\bf P(x) = {x}^{3} - 3 {x}^{2} + 4x - 12$

Putting, the Value as 3

$\red{ \implies} \tt P(3) = (3) ^{3} - 3 \times (3 {)}^{2} + 4 \times 3 - 12 \\ \\ \red{ \implies} \tt P(3) = 27 - 3 \times 9 + 12 - 12 \\ \\ \red{ \implies} \tt P(3) = \cancel{27} - \cancel{27} + \cancel{12}- \cancel{12} \\ \\ \red{ \implies} \tt P(3) = 0$

Hence, Verified

Additional Information

• When a Polynomial is solved and the value when Put equals to Zero, is said to be the zero of Polynomial.

• Polynomial having 1 as the highest degree is said to be Linear Polynomial.

• Polynomial having 2 as the highest degree is said to be Quadratic Polynomial.

• Polynomial having 3 as the highest degree is said to be Cubic Polynomial.

• Polynomial having 4 as the highest degree is said to be Bi-Quadratic Polynomial.

• If a number contains one term, it is said to be as Monomial.

• If a number contains two non-zero term, it is said to be as Binomial.

• If a number contains three non-zero term, it is said to be as Trinomial.