/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 Write the polynomial as the prod... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 66

Write the polynomial as the product of linear factors and list all the zeros of the function. $$g(x)=x^{2}+10 x+17$$

Short Answer

Expert verified
The polynomial \(g(x) = x^2 + 10x + 17\) can be expressed as \(g(x) = (x + 5 - 2鈭�2)(x + 5 + 2鈭�2)\). The zeros of the function are \(x = -5+2鈭�2\) and \(x = -5-2鈭�2\).

Step by step solution

01

Factor the Polynomial

To factor the quadratic equation, \(g(x) = x^2 + 10x + 17\), one can use the formula \(x = [-b 卤 sqrt(b虏 - 4ac)] / 2a\), where a, b and c are the coefficients of the polynomial. In this case, \(a = 1\), \(b = 10\), and \(c = 17\).\nfinding the radicand, \(b虏 - 4ac = 100 - 68 = 32\). Since the discriminant is positive, there are real and different roots. The roots are \((-10 + 鈭�32)/2=-5+2鈭�2\) and \((-10 - 鈭�32)/2=-5-2鈭�2\)
02

Write polynomial as the product of linear factors

The factorization result from Step 1 can be used to express the polynomial as the product of linear factors. This can be obtained by setting each factor equal to zero and solving for x. Therefore the polynomial can be written as: \(g(x)= (x - [-5+2鈭�2])(x - [-5-2鈭�2])\).
03

List all the zeros of the function

The zeros of the function are the x-values for which the function is equal to zero - that is, the solutions obtained in Step 1, which are \(x = -5+2鈭�2\) and \(x = -5-2鈭�2\).

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Most popular questions from this chapter

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