It is known that f (x) is an even function and a decreasing function on (0, + ∞). If f (12) > 0 > F (3), then the number of roots of F (x) = 0 is () A. 2 b. 2 or & nbsp; 1 C. 3 d. 2 or 3

It is known that f (x) is an even function and a decreasing function on (0, + ∞). If f (12) > 0 > F (3), then the number of roots of F (x) = 0 is () A. 2 b. 2 or & nbsp; 1 C. 3 d. 2 or 3

∵ f (x) is a decreasing function on (0, + ∞). If f (12) > 0 > F (3), ∵ in (12,3), the equation f (x) = 0 has a unique root, ∵ f (x) is an even function, ∵ according to the symmetry, then the equation f (x) = 0 in (- 3, - 12) has a unique root, so the number of roots of F (x) = 0 is 2, so select: a

If f (1 / 2) > 0 > F (√ 3), then the number of roots of the equation f (x) = 0 is zero

Two
If (0, + ∞) is a decreasing function and f (1 / 2) > 0 > F (√ 3), then there is a root between (1 / 2, √ 3);
Because f (x) is an even function, so f (- 1 / 2) > 0 > F (- 3), then there is a root between (- 3, - 1 / 2)

For different value ranges of M, the number of real roots of the equation x ^ 2-4 / X / + 5 = m is discussed

delta=16-4(5-m)=4(m-1)>=0---> m>=1,
1) X > = 0, the equation is: x ^ 2-4x + 5-m = 0
When m = 1, the root is double root 2, which is consistent with the equation
m> When 1, there are two real roots, the sum of which is 4 and the product is 5-m;
Therefore, 15 is two negative roots, which are consistent with each other;
m

Explore the real number solution of the equation x ^ 3-2x = 0

x^3-2x=0
x(x^2-2)=0
X (x + radical 2) (x-radical 2) = 0
The solution is: x = 0, - radical 2, radical 2