Question

The product of two zeros of a polynomial p(x)p(x)p, left parenthesis, x, right parenthesis is -3−3minus, 3.

p(x) = x^3 + 3x^2 -cx - 15p(x)=x3+3x2−cx−15p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 3, x, squared, minus, c, x, minus, 15

Find the third zero.

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Answer 1

SOLUTION

GIVEN

The product of two zeros of a polynomial p(x) is - 3

p(x) = x³ + 3x² - cx - 15

TO DETERMINE

The third zero

EVALUATION

Here it is given that the product of two zeros of a polynomial p(x) is - 3

p(x) = x³ + 3x² - cx - 15

Here

Coefficient of x³ = 1

Coefficient of x² = 3

Coefficient of x = - c

Constant term = - 15

By the given condition

Product of two zeroes = - 3

We know that

$\displaystyle \sf{Product \: of \: three \: zeroes \: = - \frac{Constant \: term}{Coefficient \: of \: \: {x}^{3} } }$

$\displaystyle \sf{ \implies \: - 3 \times \: Third \: zero \: = - \frac{ - 15}{1} }$

$\displaystyle \sf{ \implies \: - 3 \times \: Third \: zero \: = 15}$

$\displaystyle \sf{ \implies \: Third \: zero \: = \frac{15}{ - 3} }$

$\displaystyle \sf{ \implies \: Third \: zero \: = - 5 }$

FINAL ANSWER

Third zero = - 5

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