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.
Answer:
-5.2
Step-by-step explanation:
-8+1.5 = -6.5
-6.5 * 4/5 = -6.5 * 0.8 = -5.2
Answer:
<h2>A. y = 3x - 2</h2>
Step-by-step explanation:
The slope-intercept form of an equation of a line:
<em>y = mx + b</em>
<em>m</em><em> - slope</em>
<em>b</em><em> - y-intercept</em>
<em />
We have
<em>A. y = 3x - 2 - it's the slope-intercept form</em>
<em>B. x = 1/2y + 8 </em><em>NOT</em>
<em>C. 2x + 5y = 12 </em><em>NOT</em><em> - it's the standard form</em>
<em>D. 3y = 8x - 5 </em><em>NOT</em>
Answer:
64%
Step-by-step explanation:
16/25 = 0.64
0.64*100 = 64
64%
