The first one is 212
and the second one is 158
so yes it is false they do not equal
If we are supposed to assume that QS=TV
4v+3=7v-9
minus 4v both sides
3=3v-9
add 9
12=3v
divide 3
4=v
v=4
sub back
4v+3=QS=TV
4(4)+3=QS=TV
16+3=QS
19=QS=TV
then answer is C
6x+4=-11
6x=-15
X=-15/6
X=-2.5
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.
