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bonufazy [111]
3 years ago
14

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 –

2x4 + 9x3 – x2 + 12?
Mathematics
1 answer:
elena55 [62]3 years ago
7 0

Answer:


Step-by-step explanation:

Given is an algebraic polynomial of degree 5.

g(x) = 3x^5-2x^4+9x^3-x^2+12\\

Here leading term is p=3 and constant term is q =12

Factors of p are ±1,±2,±3

Factors of q are \frac{±1,±2,±3,±4,±6,±12} \\

Possible forms of p/q will be the same for any other polynomial of degree 5 with leading term =3 and constant term = 12

Hence any other polynomial

g(x) = 3x^5+ax^4+bx^3+cx^2+12

will have same possible zeroes of p/q, when a,b,c are rational.

Hence any polynomial of this type would have the same possible rational roots.

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Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number  

Answer:

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Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

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Let us solve the above quadratic equation

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Using the above formula,

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\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}

Thus the possible values of number are 7 and -4

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