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William S.'s Resources

Let's say   f(x) = 3x(x - 2)(x + 1) = 0   We know that this is true when x = 0, x = 2 and x = -1   The person who gave you this problem is very kind.  It is already factored in such a way that the identity of the zeros is manifestly obvious.

Dear Dalia,   Here we go:   P(x)=x4 - 2x3 - 13x2 - 10x   P(x) obviously = 0 when x = 0, so there is one of the real zeros.  (x = 0)   P(x) can be factored into: x(x -5 )(x + 1)(x + 2) from which it is obvious that x...

Dear Dalia,   The real roots of P(x) are as follows:   x = -(√2 + 1), x = √2 - 1 and x = 4   P(x) can be factored into (x - 4)*(x2 + 2x - 1).  From this it is easy to see that x = 4 is one of the real zeros.   (x2 + 2x -...

Dalia,   There are two and only two rational zeros of this polynomial: x = -2 and x = 4. To these we may also add x= ±√2i but I don't interpret the question of having asked for imaginary roots.

slope = m = (y1 -y2)/(x1 - x2) = [(-4) - 2]/[7 - (-8)] = (-6/15) = -(2/5)   It doesn't make any difference which point is (x1, y1) or (x2, y2) as long as you're consistent with yourself.  We could just as easily find the slope as follows:   m = [2 - (-4)]/[(-8) -...

Answers X^2+x-30=0 (answer)

x2 + x -30 = 0   This expression can be factored into   (x + 6)*(x - 5) = 0   which is true when x = -6 or x = 5.

∫ x(x2 + 2)2dx   Let u = x2 + 2   du = 2xdx   ∫ x(x2 + 2)2dx = (1/2)∫u2du = (1/2)*(u3/3) = (1/6)*(x2 + 2)3 (evaluated between 0 and 1)   = (1/6)[(1)2 + 2]3 - (1/6)[(0)2 + 2]3 = (1/6)*(27 - 8) = (19/6)

Let T = total cost of table plus chairs.   Then T = $419.99 + (6)*(199.99) = $1,619.93   Since $1,619.93 < $2,000.00 you do have enough money to complete the project.   $2,000.00 - $1,619.93 = $380.07.   The fact that you...

MinHee,   I think it would go something like this:   $785 - 10% = $706.50          (by virtue of the advanced booking)   $706.50 - 5% = $671.18       (because of the coupon)   $671...

Hi, Valerie,   (4^(1/2)) (x^(1/6)) (y^(2/3))   Well, (4^(1/2)) is easy.  That's just 2.   Now remember: when you multiply you add the exponents, so   (x^(1/6)) (y^(2/3)) = x^((1/6) +(2/3)) = x^((1/6) + (4/6)) = x^(5/6)   So   (4^(1/2))...

-8x - 5y = 10     I. 5x-15y=30         II.   Multiply Equation I. by (-3)   24x + 15y = -30     I.' -5x - 15y = 30   Add the two Equations together:   x[24...

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