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ser-zykov [4K]
2 years ago
15

Which statement is true about this quadratic equation? y=x^(2)-11x+7

Mathematics
1 answer:
Sliva [168]2 years ago
6 0

Answer: <em>This quadratic equation has two real solutions.</em>

<em />

Step-by-step explanation:

y=x^{2} -11x+7\\\\D=(-11)^{2} -4 \cdot 7=121-28=93 \: > 0\\\\x=\dfrac{11 \pm \sqrt{93} }{2}

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Alla [95]

Answer:

  -3, 1, 4 are the x-intercepts

Step-by-step explanation:

The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).

In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.

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For the given polynomial, we notice that the sum of the coefficients is zero:

  1 -2 -11 +12 = 0

This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.

Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...

  f(x) = (x -1)(x² -x -12)

We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...

  f(x) = (x -1)(x -4)(x +3)

Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.

The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.

5 0
3 years ago
Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each oth
n200080 [17]

Answer:

Rectangle or square

Step-by-step explanation:

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8 0
3 years ago
Read 2 more answers
A bag contains 15 marbles. The probability of randomly selecting a green marble is 1/5. The probability of randomly
meriva

Answer:

2

Step-by-step explanation:

well if you get all of the fractions into percentage form they will be 20%for green 8% for blue so in turn it would mean 8% of 15 is 2

3 0
3 years ago
James made a deposit in a savings account 5 years ago. The account pays 4% simple annual interest. Since then, he has earned $12
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P=i/rt
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3 0
3 years ago
The surface area of a pyramid is 327 square meters. what is the surface area of a similar pyramid that is smaller by a scale fac
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Answer:

\boxed{\text{144.33 m}^{2}}

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two pyramids.  

The ratio of the areas is the square of the scale factor.

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3 years ago
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