If x^2+bx+16 has at least one real root, then the equation x^2+bx+16=0 has at least one solution. The discriminant of a quadratic equation is b^2-4ac and it determines the nature of the roots. If the discriminant is zero, there is exactly one distinct real root. If the discriminant is positive, there are exactly two roots. The discriminant of <span>x^2+bx+16=0 is b^2-4(1)(16). The inequality here gives the values of b where the discriminant will be positive or zero:
b^2-4(1)(16) ≥ 0
</span><span>b^2-64 ≥ 0
(b+8)(b-8) </span><span>≥ 0
The answer is that all possible values of b are in the interval (-inf, -8]∪[8,inf) because those are the intervals where </span>(b+8)(b-8) is positive.
12+5=x+8
add 12 and 5
17=x+8
subtract 8 from both sides
9=x
Answer:
120
Step-by-step explanation:
The number of ways to select things from a group of things is given by the combination formula.
Where n! means n*(n-1)*(n-2)....
- There are 10 total books, so n = 10
- you have to choose 3 books, so r = 3
Plugging these into the formula gives us:
Hence, there can be 120 different groups of 3 books that u can choose from 10 books total.
Answer:
(6 * 0 + 0) + 2 /2
Step-by-step explanation: