Answer:
X = 9,X= -5, a = 2, b = -13
Step-by-step explanation:
For (1),
Using Cross-factorization,
it can be reduced to (X - 9)(X + 5) = 0
Equate each factor to 0:
we have X = 9 and X = -5
For (2),
It is the case of completing the Square,
add 4 so we get the completed square ( we want the form X^2 + 2a + a^2)
(X^2 + 4X + 4) - 9
can be simplified to (X+2)^2 -9
However since we added 4 it means we have to subtract 4
So it becomes (X+2)^2 -9 -4
= (X+2)^2 -13
All these equations are in the form of ax^2 + bx + c = 0, where a, b, and c are some numbers. the discriminants of equations like this are equal to b^2 - 4ac. if the discriminant is negative, there are two imaginary solutions. if the discriminant is positive, there are two real solutions. if the discriminant is 0, there is one real solution.
<span>x^2 + 4x + 5 = 0
</span>b^2 - 4ac
4^2 - 4(1)(5)
16-20
-4, two imaginary solutions.
<span>x^2 - 4x - 5 = 0
</span>b^2 - 4ac
(-4)^2 - 4(1)(-5)
16 + 20
36, two real solutions.
<span>4x^2 + 20x + 25 = 0
</span>b^2 - 4ac
20^2 - 4(4)(25)
400 - 400
0, one real solution.
Way 1:
a triangle with sides 3,4,5 will make a triangle. because this isn't 3,4,5 triangle it wont work.
way 2:
By using Heron's formula you can find the area of the flower bed.
<span>s=(a+b+c) ÷2
</span><span>Area =√s(s-a)(s-b)(s-c)
</span>so, 3+4+8= 15
15÷2 =7.5
√7.5(7.5-3)(7.5-4)(<span>7.5-8)
</span>Now because 7.5-8 gives you a negative number and you can't have a negative number under a square root unless you want to use an imaginary number, it won't form a triangle.
It’s (d) because if one solution to a quadratic function g is the solution given then the other solution must be it’s complex conjugate which is d.
