Step-by-step explanation:
using the quadratic formula......
Answer:
10x . . . . . (Note the sign of the middle term is negative. 10x goes in the box.)
Step-by-step explanation:
The sum of the two roots is ...
... (5 -3i) +(5 +3i) = 10
In a quadratic with leading coefficient 1, the coefficient of the 1st-degree term is the opposite of the sum of the roots. Here, that means the middle term is -10x. The minus sign is given, so the answer is 10x.
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<em>How Do We Know?</em>
When "a" and "b" are roots of a quadratic in x, it has factors (x -a)(x -b). The product of those two factors is ...
... (x -a)(x -b) = x² -(a+b)x +ab
Here, that means the product of the factors (5 -3i)(5 +3i) is ab = 34, which it is. Their sum is (a+b) = 10, so the x-term is -(a+b)x = -10x.
Step-by-step explanation:
3a²-7a−6
Factor the expression by grouping. First, the expression needs to be rewritten as 3a
2
+pa+qa−6. To find p and q, set up a system to be solved.
p+q=−7
pq=3(−6)=−18
Since pq is negative, p and q have the opposite signs. Since p+q is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −18.
1,−18
2,−9
3,−6
Calculate the sum for each pair.
1−18=−17
2−9=−7
3−6=−3
The solution is the pair that gives sum −7.
p=−9
q=2
Rewrite 3a
2−7a−6 as (3a
2−9a)+(2a−6).
(3a 2−9a)+(2a−6)
Factor out 3a in the first and 2 in the second group.
3a(a−3)+2(a−3)
Factor out common term a−3 by using distributive property.
(a−3)(3a+2)
Answer:
131.18
Step-by-step explanation:
