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3 years ago

If one of the zeroes of the cubic polynomial p(x)=ax³+bx²+cx+d is zero then find the product of other two zeroes of p(x).

Mathematics

1 answer:

Zigmanuir [339]3 years ago

6 0

Answer:

As one of the zeros of polynomial is 0, then (x-0) =x is a factor of given polynomial.

Since x is a factor , d= 0

ax^3+bx^2+cx+d = ax^3+bx^2+cx

= x(ax^2+bx+c)

Other two roots are roots of

ax^2+bx+c = 0

For a quadratic equation ax^2+bx+c = 0

Product of roots = c/a

Sum of roots = -b/a

Product of other two roots = c/a

Hope this helps :D

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Work out the nth of this sequence:

Gekata [30.6K]

Answer:

$a_n = -11 +3(n -1)$

Explanation:

The $n$ th term of an arithmetic sequence is explicitly defined as $a_n = a_1 +d(n -1)$ where $a_1$ is the first term of the sequence and $d$ is the the common difference.

From the given first five terms of the sequence we can see that the first term is $11$ so $a_1 = 11$ .

The common difference, $d$ , can be calculated by $a_n - a_{n -1}$ so we'll find the common difference of the given sequence by letting $n = 2$

$d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = -8 -(-11) \\ d = -8 +11 \\ d = 3$ .

Now let's plug everything we know.

$a_1 = -11$

$d = 3$

$a_n = -11 +3(n -1)$

6 0

3 years ago

A skateboard ramp has a slope of 4/9. What is the measure of the angle the ramp forms with the ground

Mama L [17]

Answer:

Step-by-step explanation:

tanθ = 4/9

θ = arctan(4/9) ≈ 23.96°

7 0

3 years ago

An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

5 0

3 years ago

A cylinder has a volume of 245 cubic units and a height of 5 units. The diameter of the cylinder is

frutty [35]

The independent variable here is b, the number of mats; the dependent var. is p, the cost of b mats. Thus, p = f(b).

Here, 245 units^3 = pi*r^2*(5 units), or

245 units^3

r^2 = ------------------- = 15.61 units^2. Thus, the radius is sqrt(15.61 units^2), or

5(3.14) units 3.95 units. The DIAMETER is d = 2*r = 7.90 units.

8 0

4 years ago

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When the median of a data set 110 and the mean is 127, what does it mean?

ss7ja [257]

The percentile associated with the mean must be high than 50%

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3 years ago

If one of the zeroes of the cubic polynomial p(x)=ax³+bx²+cx+d is zero then find the product of other two zeroes of p(x).​

If one of the zeroes of the cubic polynomial p(x)=ax³+bx²+cx+d is zero then find the product of other two zeroes of p(x).