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zloy xaker [14]
3 years ago
12

What point is an x-intercept of the quadratic function f(x)=(x+6)(x-3)

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
7 0
X-intercept is (-6, 0) , (3, 0)

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These roots of the polynomial equation x^4-4x^3-2x^2+12x+9=0 are 3,-1,-1. Explain why the fourth root must be a real number. Fin
Alex787 [66]

Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.

Because we know 3 and -1 (multiplicity 2) are both roots, the last root r is such that we can write

x^4-4x^3-2x^2+12x+9=(x-3)(x+1)^2(x-r)

There are a few ways we can go about finding r, but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be (-3)(1)(1)(-r)=3r.

Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have

3r=9\implies r=3

so the missing root is 3.

Other things we could have tried that spring to mind:

- three rounds of division, dividing the quartic polynomial by (x-3), then by (x+1) twice, and noting that the remainder upon each division should be 0

- rational root theorem

4 0
3 years ago
Read 2 more answers
Point B is halfway between A and C. The distance from C to D is the same as the distance from D to E, which is the same as the d
jek_recluse [69]

Answer:

60

Step-by-step explanation:

area of triangle ACF is (1/2) (AC) (CF) = 180

area of triangle BCE = (1/2) (BC) (CE)

BC = AC/2

CE=(2/3) CF

so (1/2) (BC) (CE) = (1/2) (AC/2) (2/3)CF = (1/2)(2/3)(180) = 60 sq cm

8 0
2 years ago
Which one of the following is not a integer<br><br> A-5<br> B.-3<br> C-1/2<br> D-10
Karolina [17]
-1/2 is not a integer
4 0
3 years ago
Read 2 more answers
What is the answer please tell me!
slava [35]

Answer:

add all of the absolute deviations and divide by the number of swimmers

Step-by-step explanation:


5 0
3 years ago
Solve for the values of x and y in each item to make the given quadrillater a parallelogram​
maria [59]

Answer:

For given parallelogram, the value of x = 114° and y = 66°

Step-by-step explanation:

(Refer figure)

Given quadrilateral ABCD is a parallelogram.

m∠A = 66°

m∠B = x°

m∠C = y°

m∠D = 114°

Since by properties of parallelogram, the both pairs of opposite sides of a parallelogram are parallel.

Opposite angles of a parallelogram are congruent ...........................(1)

Consecutive angles of a parallelogram are supplementary ................(2)

Using (1) for given parallelogram ABCD; we get,

m∠B = m∠D

m∠A = m∠C

Therefore x = 114° and y = 66°.

Using (2) to check whether the two consecutive angles are supplementary.

( m∠A + m∠D ) =  ( m∠B + m∠C ) = ( m∠C + m∠D ) = 66° + 114° = 180°

Hope it helps!!

3 0
3 years ago
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