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Murrr4er [49]
3 years ago
12

What is the answer to this question? 1.4a^2+4a-63

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
3 0

Answer:

Step-by-step explanation:

Δ = 4^{2}  - 4 * 4 * (-63)  =  16 + 16 * 63 = 16 * (1 + 63) = 16 * 64

VΔ = 4 *  8 = 32

a = (- 4 ± 32) * \frac{1}{8}

a' = 7/2

a''= 9/2

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Find all solutions to x³+3x² − 9x − 27 = 0 by factoring the equation.
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Answer:

The solutions are x=-3,\:x=3

Step-by-step explanation:

To factor this cubic polynomial x^3+3x^2-9x-27 you must:

  • Group the polynomial into two sections

x^3+3x^2-9x-27=\left(x^3+3x^2\right)+\left(-9x-27\right)

  • Factor out -9 from (-9x-27)

(-9x-27)=-9\left(x+3\right)

  • Factor out x^2 from (x^3+3x^2)

(x^3+3x^2)=x^2\left(x+3\right)

x^3+3x^2-9x-27=-9\left(x+3\right)+x^2\left(x+3\right)

  • Factor out common term x+3

-9\left(x+3\right)+x^2\left(x+3\right)=\left(x+3\right)\left(x^2-9\right)

x^3+3x^2-9x-27=\left(x+3\right)\left(x^2-9\right)

  • Factor x^2-9

x^2-9=\left(x+3\right)\left(x-3\right)

x^3+3x^2-9x-27= \left(x+3\right)\left(x+3\right)\left(x-3\right)

x^3+3x^2-9x-27=\left(x+3\right)^2\left(x-3\right)=0

  • Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0

x+3=0, \quad{x=-3}\\x-3=0, \quad{x=3}

The solutions are

x=-3,\:x=3

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