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3 years ago

What are the roots of the equation 16x2 + 40x + 27 = 0 in simplest a + bi form?

Mathematics

1 answer:

bezimeni [28]3 years ago

7 0

9514 1404 393

Answer:

-5/4 +i(√2)/4 and -5/4 -i(√2)/4

Step-by-step explanation:

I find simplest form to be easier to get to if the leading coefficient is 1. Dividing by 16, we have ...

x^2 +5/2x +27/16 = 0

Completing the square by adding and subtracting the square of half the x-coefficient, we get ...

(x^2 +5/2x +25/16) +27/16 -25/16 = 0

(x +5/4)^2 = 2/16

Subtracting 2/16, taking the square root, and subtracting 5/4 gives ...

x +5/4 = ±√(-2/16)

x = -5/4 ±i(√2)/4

The roots are -5/4 +i(√2)/4 and -5/4 -i(√2)/4.

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3 years ago

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ANSWER

$y = 3 \pm \sqrt{21}$

EXPLANATION

The quadratic equation is:

${y}^{2} - 6y - 12 = 0$

Group variable terms:

${y}^{2} - 6y = 12$

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