Proof: the equation x2 + MX + 1 = 0 of X has two negative real roots if and only if M ≥ 2
The following results are proved: (1) sufficiency: ∵ m ≥ 2, ∵ (?) = M2-4 ≥ 0, the equation x2 + MX + 1 = 0 has real roots. Let two of x2 + MX + 1 = 0 be x1, x2. According to Weida's theorem, ∵ X1 + x2 = - M ≤ - 2, ∵ x1, X2 are both negative roots
RELATED INFORMATIONS
- 1. If the difference between the two equations 2x ^ 2 - (k-1) x + K + 3 = 0 is 1, what is the value of K? The absolute value of (x1-x2) = the absolute value of B ^ 2-4ac / a [this is a theorem. So, 1 = (k-1) ^ 2-8 (K + 3) It's wrong. I must be very wrong! I'd like to know what's wrong with me.
- 2. If the difference between the two equations 2x2 - (K + 1) x + K + 3 = 0 is 1, then the value of K is 1______ .
- 3. If the difference between the two equations x ^ 2 + 2x + K + 1 = 0 is 2 √ 3, then the value of K is
- 4. Excuse me, the square of (2x + 1) minus 5 is equal to 0, the solution equation is? Ask God for help
- 5. Given that the square of equation 2x + 3x + m is equal to two real roots of 0, one of which is twice of the other, we can help you to find the value of M
- 6. Given that the square difference of the two equations x ^ 2-4x + 6K = 0 is equal to 8, then K is equal to 0 I got half of it
- 7. It is known that the two square differences of the X equation x & sup2; + 2x + 1-k & sup2; = 0 are equal to 2, and the value of K is obtained
- 8. If the difference between the two equations 2x2 - (K + 1) x + K + 3 = 0 is 1, then the value of K is 1______ .
- 9. It is known that the reciprocal sum of the two equations x-2x + k = 0 is 8 / 3,
- 10. On the equation MX ^ 2-2x + 1 = 0 of X, there is only one real number root, find M
- 11. Proof: the equation x2 + MX + 1 = 0 of X has two negative real roots if and only if M ≥ 2
- 12. The equation AX2 + 2x + 1 = 0 has at least one negative real root if and only if () A. 0 < a < 1b. 0 < a ≤ 1 or a < 0C. 0 ≤ a ≤ 1D. A ≤ 1
- 13. If α and β are the two real roots of the equation x + 2x-2010 = 0, find the square of α + 3 α + β Factorization in real numbers: the square of 1-xy-4x, the square of Y Solution equation: (2-radical 3) square of X-2 (radical 3-1) X-6 = 0
- 14. If the two real number roots of the equation x2 + (M-3) x + M = 0 about X are unequal positive numbers, then the value range of real number m is______ .
- 15. If the two roots of the equation X2 (is square) + (T-2) x + 5-T = 0 of X are greater than 2, then the value range of T is________
- 16. The combination a consists of the solution of the equation AX & # 178; - 2x + 1 = 0. 1. If the set a is an empty set, find the value range of the real number a 2. If there is only one element in the set a to find the value of a, I hope you can help me. I'm not good at math. I'm a beginner
- 17. It is known that the equation x ^ 2-4x + 2a-6 = 0 about X has a negative solution, so we can find the value range of the real number a
- 18. The two of the equation x ^ 2 + 2 (P + 1) x + 2p-5 = 0 are both negative numbers. The value range of the real number P is obtained
- 19. If the solution of the equation 3a-4x = 6 of X is nonnegative, then the value range of a is
- 20. If the solution of equation 5 (A-1) = 3A + X-11 is nonnegative, then the value range of a is?