Math, asked by Anonymous, 9 months ago

Polynomial p is defined by
p(x)=x3+5x2−2x−24p
has a zero at x = 2. Factor p completely and find its zeros.​

Answers

Answered by Anonymous
12

solution

p(x) has a zero at x = 2 and therefore x - 2 is a factor of p(x).

★ Divide p(x) by x - 2

→ p(x) / (x - 2) = (x² + 5 x² - 2 x - 24) / (x- 2)x2 + 7 x + 12

Using the division above, p(x) may now be written in factored form as follows:

→ p(x) = (x - 2)(x2 + 7 x + 12)

Factor the quadratic expression

→ x² + 7 x + 12.

→ p(x) = (x - 2)(x + 3)(x + 4)

The zeros are found by solving the equation.

→ p(x) = (x - 2)(x + 3)(x + 4) = 0

For p(x) to be equal to zero, we need to have

→ x - 2 = 0 , or x + 3 = 0 , or x + 4 = 0

Solve each of the above equations to obtain the zeros of p(x).

→ x = 2 , x = - 3 and x = -4\sf

Answered by sp6559568
40

 \huge \star \underline \red{question}

Q..Polynomial p is defined by

p(x)=x3+5x2−2x−24p

has a zero at x = 2. Factor p completely and find its zeros.

 \huge \star \bold \red{solution}

p(x) has a zero at x = 2 and therefore x - 2 is a factor of p(x).

⚘Divide p(x) by x - 2

→ p(x) / (x - 2) = (x² + 5 x² - 2 x - 24) / (x- 2)x2 + 7 x + 12

⚜Using the division above, p(x) may now be written in factored form as follows:

→ p(x) = (x - 2)(x2 + 7 x + 12)

Factor the quadratic expression

→ x² + 7 x + 12.

→ p(x) = (x - 2)(x + 3)(x + 4)

The zeros are found by solving the equation.

→ p(x) = (x - 2)(x + 3)(x + 4) = 0

For p(x) to be equal to zero, we need to have

→ x - 2 = 0 , or x + 3 = 0 , or x + 4 = 0

Solve each of the above equations to obtain the zeros of p(x).

→ x = 2 , x = - 3 and x = -4

 \large \star \underline \green{hope \: it \: helps \: u \: siso}

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