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2 years ago

According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.

Mathematics

1 answer:

Andrei [34K]2 years ago

7 0

Answer:

The answer is 3 and (-4).

Step-by-step explanation:

We are given an equation 2x² + 2x – 24.

Let us assume that the equation is equal to zero.

2x² + 2x – 24 = 0

Now, divide whole equation by 2 we get,

x² + x – 12 = 0

x² + 4x – 3x – 12 = 0

x(x + 4) – 3(x + 4) = 0

(x – 3) (x + 4) = 0

x = 3, -4

Thus, The actual roots of f(x) are 3 and (-4).

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I am joyous to assist you anytime.

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3 years ago

(2m2+10m+1) from (−8m2−8m+12)

m_a_m_a [10]

Answer:

4mfro• (2m2+10m+1)•(2m2+2m-3)

STEP

Equation at the end of step 1

0-((((((((2•(m2))+10m)+1)•f)•r)•o)•m)•(((0-23m2)-8m)+12))

STEP

Equation at the end of step

0-(((((((2m2+10m)+1)•f)•r)•o)•m)•(-8m2-8m+12))

STEP

Trying to factor by splitting the middle term

3.1 Factoring 2m2+10m+1

The first term is, 2m2 its coefficient is 2 .

The middle term is, +10m its coefficient is 10 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 2 • 1 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 10 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3

2 + 1 = 3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

0-((((f•(2m2+10m+1)•r)•o)•m)•(-8m2-8m+12))

STEP

Equation at the end of step 4

0-(((fr•(2m2+10m+1)•o)•m)•(-8m2-8m+12))

STEP

Equation at the end of step 5

0-((fro•(2m2+10m+1)•m)•(-8m2-8m+12))

STEP

Equation at the end of step 6

0 - (mfro • (2m2 + 10m + 1) • (-8m2 - 8m + 12))

STEP

Pulling out like terms

8.1 Pull out like factors :

-8m2 - 8m + 12 = -4 • (2m2 + 2m - 3)

Trying to factor by splitting the middle term

8.2 Factoring 2m2 + 2m - 3

The first term is, 2m2 its coefficient is 2 .

The middle term is, +2m its coefficient is 2 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 2 .

-6 + 1 = -5

-3 + 2 = -1

-2 + 3 = 1

-1 + 6 = 5

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

0 - -4mfro • (2m2 + 10m + 1) • (2m2 + 2m - 3)

STEP

Final result :

4mfro • (2m2 + 10m + 1) • (2m2 + 2m - 3)

5 0

3 years ago

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