Pls answer this questions;?

Question

1.What is the sum of the roots of 3x^2-7x+8=0?
a. 3/7 b. -7/3 c. 7/3 d. -3/7
2. What is the remainder when P(x)=x^3-7x+5 is divided by x-1?
a. -1 b. 1 c. 5 d. -5
3. Factor completely: x^3-6x^2+3x+10
4. What is the range of the function y+x^2-3x-10?
5.If P(x) is a polynomial with a positive degree, then P(x) has at least one zero.
a. the number root theorem
b. The fundamental theorem of algebra
c.The remainder theorem
d. the factor theorem
6. It occurs whenever 2 successive terms have opposite signs?
7. what is the formula of the division algorithm?
8. The domain of the quadratic function
a. the set of all real numbers
b. the set of positive and real numbers
c. the set of integers
d. the set of negative real numbers
9. How many turning points does the equation x^8-5x^2-2x+1 have?
10. Transform f(x)= -2x^2-16x+12 into vertex form.

Answer 1

1. If you write it as ax^2 + bx + c, then the two roots are:

[ -b + SQRT( b^2 - 4ac )] / 2a and
[ -b + SQRT( b^2 - 4ac )] / 2a

adding them together, the SQRT part cancels (+ and -)

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2. Just do it in parts: (and put in a 0 x^2 to fill in all degrees)

x^3 + 0 x^2 divided by (x-1) = x^2, leaving x^2
(because x^3 = x^2(x-1) + x^2)

To the remainder, add on the next term:
x^2 -7x divided by (x-1) = x, leaving -6x

-6x +5 divided by (x-1) = -6, leaving ??
because -6x + 5 = -6(x-1) + ??

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3. The trick is to find a first root (any root). It appears that x = -1 is a root, because (-1)^3 -6(-1)^2 +3(-1) + 10 = -1 -6 -3 + 10 = 0
therefore, x+1 (= 0) should be a factor

Divide the polynomial by (x+1)

This will leave you a quadratic (second degree) which is easier to solve (and you can apply the same trick again).

4. Domain is where values of x can come from.
Range is where the values of the function can go.
If you really mean y+x^2-3x+10, then it can be anything (because of y).
However, I suspect that you meant y = x^2-3x-10. This is a quadratic with branches pointing up (because the factor of the x^2 is positive); therefore, it will have a minimum.

One way to find the minimum is to differentiate the equation:
dy/dx = 2x -3
This is equal to zero at the minimum point
2x-3 = 0
2x = 3
x = 3/2

the range is from y(3/2) [meaning: the value of y when x = 3/2] up to + infinity.

5. In real numbers, the statement is false.
x^2 + 15 (a polynomial of positive degree) does not have a zero in real numbers.
The statement is true in complex numbers, because you can factor any polynomial of any degree into first degree complex factors.

9. At a 'turning point', the differential is zero. The differential of an eight degree polynomial is a seventh degree polynomial.