Quadratic equation which has no solution gives zero for the value of d.
d = b² - 4ac
0 = 3² +- 4(-1)c
-9 = +_ 4c
c = -9/-4 pr 9/-4
c = 9/4 or -9/4
In short, Your Answers would be Option C & E
Hope this helps!
Answer:
Whats the question?
Step-by-step explanation:
25d - 250 | - 575d^2 + 2277d + 34362
p.s. Excuse the scribble.
Step-by-step explanation:
This is a piece-wise function. The three intervals we need to worry about are [0, 1), [1,2], and [2,4].
Separate the functions into their pieces and draw out the individual graphs. Place them together onto the graph within their respective intervals.
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
