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3 years ago

Find the discriminant and the number of real roots for this equation.

Mathematics

1 answer:

Margaret [11]3 years ago

6 0

Our discriminant is 0 so, $4x^2 + 12x + 9 = 0$ has one real root.

Option C is correct.

Step-by-step explanation:

we need to find the discriminant and the number of real roots for the following equation:

$4x^2 + 12x + 9 = 0$

The discriminant is found by using square root part of quadratic formula:

$b^2-4ac$

where b =12, a=4 and c=9

Putting values:

$=b^2-4ac\\=(12)^2-4(4)(9)\\=144-144\\=0$

To find out the number of real roots using discriminant we have following rules:

if discriminant b^2-4ac >0 then 2 real roots
if discriminant b^2-4ac =0 then 1 real root
if discriminant b^2-4ac <0 then no real roots

Since our discriminant b^2-4ac is 0 so, $4x^2 + 12x + 9 = 0$ has one real root.

Option C is correct.

Keywords: discriminant

Learn more about discriminant at:

#learnwithBrainly

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Determine between which consecutive integers the real zeros of y(x) = x2 - 4x – 2 are located.

Sholpan [36]

Answer:

The zeros are x1=4.45 and x2=-0.45.

x1 is between 4 and 5.

x2 is between -1 and 0.

Step-by-step explanation:

We have the function:

$y(x) = x2 - 4x-2$

As this is a quadratic function, we can calculate the zeros of the function with the quadratic equation:

$x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1\cdot(-2)}}{2\cdot 1}\\\\\\x=\dfrac{4\pm\sqrt{16+8}}{2}\\\\\\x=\dfrac{4\pm\sqrt{24}}{2}\\\\\\x=\dfrac{4\pm4.9}{2}=2\pm2.45\\\\\\x_1=2+2.45=4.45\\\\x_2=2-2.45=-0.45$

The zeros are x1=4.45 and x2=-0.45.

x1 is between 4 and 5.

x2 is between -1 and 0.

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How many Children attended the classroom if there were 11 girls who made up 44% of the children?

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Answer:

Step-by-step explanation:

If 11 equals 44%, then x equals 100%.

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9. The 10,000 seat stadium is 89% full. How many people are watching the game inside the stadium? with solution pls.

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Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar

Brrunno [24]

The distance between the two points is $d=8.6m$

The polar coordinate of A is $\left(4.47,296.57\right)$

The polar coordinate of B is $\left(4.24,135\right)$

Explanation:

The two points are $A(2,-4)$ and $B(-3,3)$

The distance between two points is given by,

$d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6$

Thus, the distance between the two points is $d=8.6m$

The polar coordinates of A can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $A(2,-4)$ , we get,

Distance = $\sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43$

To make the angle positive, let us add 360,

$\theta=360-63.43=296.57$

The polar coordinate of A is $\left(4.47,296.57\right)$

Similarly, The polar coordinate of B can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $B(-3,3)$ , we get,

Distance = $\sqrt{(3)^{2}+(3)^{2}}=4.24$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45$

To make the angle positive, let us add 360,

$\theta=180-45=135^{\circ}$

The polar coordinate of B is $\left(4.24,135\right)$

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