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2 years ago

The equation 12x² + 4kx + 3 = 0 has real and equal roots, if

Mathematics

1 answer:

sleet_krkn [62]2 years ago

8 0

Answer:

$k=\pm3$

Step-by-step explanation:

[...] if you can write the LHS as a perfect square, or if you can't spot a factorization of it right away, if and only if the discriminant $\Delta = b^2-4ac$ (or, if b is an even number, 1/4 of it) is zero.

Stare at it for a while. First term is $3(2x)^2$ , third term is $3(1)^2$ , we are missing a double product, but we can play with k. For the LHS to be $3(2x\pm1)^2 = 3(4x^2\pm4x+1) = 12x^2\pm12x+3$ you just need $4k= \pm12 \rightarrow k=\pm3$ .

Then number crunching it is. Set the discriminant to 0, solve for k

$\frac{\Delta}4 = 4k^2-12\cdot 3 =0 \rightarrow 4k^2=36 \\k^2 = 9 \rightarrow k=\pm3$

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A flagpole broke in a storm. It was originally 81 8181 feet tall. 28 2828 feet are still sticking straight out of the ground, wh

solong [7]

Answer:

The end of the flagpole is 50.79 ft away from the base of the pole.

Step-by-step explanation:

The problem is represented by the diagram below.

The broken flagpole forms the shape of a right angled triangle. We need to find one of the sides of the triangle, the adjacent (x).

The hypotenuse is the broken part of the flagpole (53 ft), while the opposite is the part of the flagpole that is still stuck to the ground (28 ft).

Using Pythagoras theorem, we have that:

$hyp^2 = adj^2 + opp^2$

=> $53^2 = x^2 + 28^2$

$3364 = x^2 + 784\\\\=> x^2 = 3364 - 784\\\\x^2 = 2580\\\\x = \sqrt{2580}\\ \\x = 50.79 ft$

The end of the flagpole is 50.79 ft away from the base of the pole.

7 0

3 years ago

Please help fast!!!!! 20 points

FromTheMoon [43]

Answer:

I think the answer is B.7070-(-7460)

I'm sorry if it was wrong..

4 0

3 years ago

Read 2 more answers

The television coverage of the soccer f.a. Final begin at 2:05 a.m. and finished an hour after 50 minutes later what was the tim

son4ous [18]

Answer: 3:55 am is correct

8 0

3 years ago

Express the given terminating decimal as a quotient of integers. if possible, reduce to lowest terms. 0.66

taurus [48]

.66 is 66 out of 100. "out of" means divide

66/100
We can reduce this by dividing each number by the same amount - 2

33/50

8 0

3 years ago

Find two numbers that have a sum of -2 and a product of -48 (please show work if possible)

andreev551 [17]

Answer: -8 and 6

Step-by-step explanation:

factors of 48: 1,2,4,6,8,12,24,48

1 x 48

2 x 24

4 x 12

6 x 8

for a negative product, one of the factors must be negative and the other positive.

for two number to have a sum of -2, the greater number must be the negative number, and both numbers should have be two values apart (ex. 6 and 8, 3 and 5, 12 and 14, etc.). In this case, 8 would have to be negative whereas 6 will be left positive.

and then we check:

-8 x 6 = 48

-8 + 6 = -2

5 0

3 years ago