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Reptile [31]
3 years ago
6

If a quadratic equation with real coefficients has a discriminant of 3 then the two roots must be

Mathematics
1 answer:
lukranit [14]3 years ago
6 0

In a quadratic equation

q(x) = ax^2 + bx + c 

The discriminant is = b^2 - 4ac

We have that discriminant = 3

If b^2 - 4ac > 0, then the roots are real.

If b^2 - 4ac < 0 then the roots are imaginary

<span>In this problem b^2 - 4ac > 0   3 > 0 </span>

then the two roots must be real

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What are the solutions of x^2-2x+5=0
sweet [91]

The solution of x^{2}-2 x+5=0 are 1 + 2i and 1 – 2i

<u>Solution:</u>

Given, equation is x^{2}-2 x+5=0

We have to find the roots of the given quadratic equation

Now, let us use the quadratic formula

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}  --- (1)

<em><u>Let us determine the nature of roots:</u></em>

Here in x^{2}-2 x+5=0 a = 1 ; b = -2 ; c = 5

b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16

Since b^2 - 4ac < 0 , the roots obtained will be complex conjugates.

Now plug in values in eqn 1, we get,

x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \times 1 \times 5}}{2 \times 1}

On solving we get,

x=\frac{2 \pm \sqrt{4-20}}{2}

x=\frac{2 \pm \sqrt{-16}}{2}

x=\frac{2 \pm \sqrt{16} \times \sqrt{-1}}{2}

we know that square root of -1 is "i" which is a complex number

\begin{array}{l}{\mathrm{x}=\frac{2 \pm 4 i}{2}} \\\\ {\mathrm{x}=1 \pm 2 i}\end{array}

Hence, the roots of the given quadratic equation are 1 + 2i and 1 – 2i

6 0
3 years ago
Carlotta has 12 2/3 yd of ribbon to be divided among 19 girls in the cheerleading squad.how much ribbon will each girl get if it
trasher [3.6K]

Answer:

Each girl gets 2/3 yd of ribbon.

Step-by-step explanation:

12 2/3=38/3

(38/3)/19

(38/3)(1/19)

(2/3)(1/1)=2/3

4 0
3 years ago
Last week you watch four hours of TV this week you watched eight hours TV place points on the graph to show your activity for la
LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

You should place a point on the graph at 4 for four hours of TV last week. And place a point at 8 for eight hours of TV this week.

8 0
3 years ago
Tim runs 3 miles every 45 minutes. At this rate, how long did it take Tim to run 18 miles?
geniusboy [140]

Answer: 270 minutes or 4 hours and 30 minutes

Step-by-step explanation: 3x6 =18  and 45 x 6= 270

7 0
3 years ago
A cube has a volume of 64 cubic meters what is the length of each edge
Murljashka [212]

Answer:

The length of each side is 4 m

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

64 = s^3

Take the cube root of each side

64 ^ (1/3) = s^3 ^ (1/3)

4 = s

The length of each side is 4 m

7 0
3 years ago
Read 2 more answers
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