Answer:
x^2+4x-32=0
(mid-term breaking---4 x 8=32)
x^2+8x-4x-32=0
x(x+8)-4(x+8)
x+8=0 or x-4=0
So x=+4 or x=-8
Step-by-step explanation:
Answer:
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Step-by-step explanation:
Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer:
C
Step-by-step explanation:
I substituted the x value with the different options. I kept doing that until the equation made sense.
Answer: r=6.5
Step-by-step explanation:
-2r = -13
r = 13/2
r = 6.5
