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mr_godi [17]
4 years ago
12

Which equation has the solutions x = -3 ± √3i/2 ?

Mathematics
1 answer:
Maurinko [17]4 years ago
6 0

Answer:Answer is option C : [x^{2} + 3x + 3 ] =0

Note:  None of options matches with given question.

instead of "-3" , there should be "-\frac{3}{2}".

Step-by-step explanation:

Note:  None of options matches with given question.

instead of "-3" , there should be "\frac{3}{2}".  

Here, First thing you have to observe the nature of roots.

∴ x = -\frac{3}{2}+\frac{\sqrt{3}}{2}i and x = -\frac{3}{2}-\frac{\sqrt{3}}{2}

∴ [ x+(\frac{3}{2}-\frac{\sqrt{3}}{2}i) ][ x+(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ]=0

∴ [ x^{2} + x(\frac{3}{2}+\frac{\sqrt{3}}{2}i)+ x(\frac{3}{2}-\frac{\sqrt{3}}{2}i) + (\frac{3}{2}-\frac{\sqrt{3}}{2}i)(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ]=0

∴ [x^{2} + \frac{3}{2}x + \frac{\sqrt{3}}{2}ix + \frac{3}{2}x - \frac{\sqrt{3}}{2}ix + (3-\frac{\sqrt{3}}{2}i)(3+\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + (\frac{3}{2}-\frac{\sqrt{3}}{2}i)(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + \frac{9}{4} - (\frac{\sqrt{3}}{2}i)(\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + \frac{9}{4} - (\frac{3}{4}) i^{2} ] =0

∴ [x^{2} + 3x + \frac{9}{4} + (\frac{3}{4}) ] =0

∴ [x^{2} + 3x + \frac{12}{4} ] =0  

∴ [x^{2} + 3x + 3 ] =0  

Thus, Answer is option C : <em>[x^{2} + 3x + 3 ] =0  </em>

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Which ordered pairs are solutions to the inequality y - 3x &lt; -8?
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Answer:

Option B,C and E are solution to given inequality y - 3x < -8

Step-by-step explanation:

We need to check which ordered pairs from given options satisfy the inequality y - 3x < -8

Ordered pairs are solutions to inequality if they satisfy the inequality

Checking each options by pitting values of x and y in given inequality

A ) (1, -5)

-5-3(1)

So, this ordered pair is not the solution of inequality as it doesn't satisfy the inequality.

B) (-3, - 2)

-2-3(-3) < -8\\-2-9

So, this ordered pair is solution of inequality as it satisfies the inequality.

C) (0, -9)

-9-3(0)

So, this ordered pair is solution of inequality as it satisfies the inequality.

D) (2, -1)

-1-3(2)

So, this ordered pair is not the solution of inequality as it doesn't satisfy the inequality.

E) (5, 4)​​​

4-3(5)

So, this ordered pair is solution of inequality as it satisfies the inequality.

So, Option B,C and E are solution to given inequality y - 3x < -8

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2 years ago
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