Mathematics, 30.09.2019 15:00 loroloco71

What are the roots of y = x2 – 3x – 10?
–3 and –10
–2 and 5
2 and –5
3 and 10

Answers: 2

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Answer from: aletadaboss

The polynomial factors to (x - 5)(x + 2)
Set each factor = 0
x = 5, x = -2

Answer from: boo3972

B. -2 and 5

Step-by-step explanation:

We are given the quadratic equation y=x^2-3x-10

The roots are given when we equate the polynomial to 0 i.e. x^2-3x-10=0

The roots of a quadratic equation ax^2+bx+c=0 is given by $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

On comparing the equations, we have,

a= 1, b= -3 and c= -10

Substituting the values in the formula gives us,

$x=\dfrac{3\pm \sqrt{(-3)^2-4\times 1\times (-10)}}{2\times 1}\\\\x=\dfrac{3\pm \sqrt{9+40}}{2}\\\\x=\dfrac{3\pm \sqrt{49}}{2}\\\\x=\dfrac{3\pm 7}{2}\\\\x=\dfrac{3+7}{2},\ x=\dfrac{3-7}{2}\\\\x=\dfrac{10}{2},\ x=\dfrac{-4}{2}\\\\x=5,\ x=-2$

Thus, the roots of the equation are 5 and -2.

So, option B is correct.

Answer from: Quest

5. y=6; de=7; fg=8

6. x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

y = 6

of course, the total chord length is the sum of the lengths of its segments.

de = dh +eh = 3+4 = 7

fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

x = lk = mk×nk/jk = 6×7/10 = 4.2

jl = jk +lk = 10 +4.2 = 14.2

mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

Find the value of the variable and the length of each chord for #5 and #6.

Answer from: Quest

i dont know

step-by-step explanation:

What intervals is the function increasing? decreasing?

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What are the roots of y = x2 – 3x – 10?
–3 and –10
–2 and 5
2 and –5
3 and...

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