Bunuel wrote:
1. If \(x=\sqrt[4]{x^3+6x^2}\), then the sum of all possible solutions for x is:A. -2
B. 0
C. 1
D. 3
E. 5
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009482. The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0 is 3. What is the value of b?A. -64
B. -16
C. -15
D. -1/16
E. -1/64
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009503. If a and b are positive numbers, such that a^2 + b^2 = m and a^2 - b^2 = n, then ab in terms of m and n equals to:A. \(\frac{\sqrt{m-n}}{2}\)
B. \(\frac{\sqrt{mn}}{2}\)
C. \(\frac{\sqrt{m^2-n^2}}{2}\)
D. \(\frac{\sqrt{n^2-m^2}}{2}\)
E. \(\frac{\sqrt{m^2+n^2}}{2}\)
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009564. What is the maximum value of -3x^2 + 12x -2y^2 - 12y - 39 ?A. -39
B. -9
C. 0
D. 9
E. 39
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009625. If x^2 + 2x -15 = -m, where x is an integer from -10 and 10, inclusive, what is the probability that m is greater than zero?A. 2/7
B. 1/3
C. 7/20
D. 2/5
E. 3/7
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009706. If mn does not equal to zero, and m^2n^2 + mn = 12, then m could be:I. -4/n
II. 2/n
III. 3/n
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009737. If x^4 = 29x^2 - 100, then which of the following is NOT a product of three possible values of x? I. -50
II. 25
III. 50
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009758. If m is a negative integer and m^3 + 380 = 381m , then what is the value of m?A. -21
B. -20
C. -19
D. -1
E. None of the above
Solution: https://gmatclub.com/forum/new-algebra- ... l#p12009809. If \(x=(\sqrt{5}-\sqrt{7})^2\), then the best approximation of x is:A. 0
B. 1
C. 2
D. 3
E. 4
Solution: https://gmatclub.com/forum/new-algebra- ... l#p120098210. If f(x) = 2x - 1 and g(x) = x^2, then what is the product of all values of n for which f(n^2)=g(n+12) ?A. -145
B. -24
C. 24
D. 145
E. None of the above
Solution: https://gmatclub.com/forum/new-algebra- ... l#p1200987Kudos points for each correct solution!!! 2. The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0 is 3. What is the value of b?
A. -64
B. -16
C. -15
D. -1/16
E. -1/64
A quick way to solve this question, without having to find the value of a by substituting 3 in to equation 2 is to simply see that the second equation's constant value is 15. The roots of the second equation will have to equal 15 (think about what you do when factoring quadratic equations e.g. to find factors of ax^2 + bx + c you will look for two factors of AC that in some way add up to b).
So the other factor of the second equation is 5, because 3x5=15. So we know that a will be equal to 5 + 3 = 8. Once you know that you can rewrite the first equation as x^2 +
8x - b. Now remember that equation 1 has equal roots which means it follows the form of (a+b)^2 which expands to a^2 + 2ab + b^2.
Therefore a=2*1*4 (1 is the coefficient of x^2, and if a = 2 * first expression * second expression then a = 2*1*
4).
Hence b = 4^2= 16 (think about the (a+b)^2 form again). The negative sign is needed so the expression follows this form.Answer is thus B -16