Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If the sum of the roots of the equation 1 2x+p + 1 2x+q = 1 r is zero, then what is r equal to?
- Let and be the roots of the equation ax^2+bx+c=0 and p_n= ^n+ ^n, where n>1. What is ap_ n+1 +bp_n+cp_ n-1 equal to?
- If x^2-2x +1=0, then what is the magnitude of x?
- If the roots of the quadratic equation x^2+2x+k=0 are real, then
- If and are the roots of the equation 4x^2+2x-1=0, then which one of the following is correct?
- If one root of 5x^2+26x+k=0 is reciprocal of the other, then what is the value of k?
- If k is one of the roots of the equation x(x+1)+1=0, then what is its other root?
- The quadratic equation 3x^2-(k^2+5k)x+3k^2-5k=0 has real roots of equal magnitude and opposite sign. Which one of the following...
- If p and q are the non-zero roots of the equation x^2+px+q=0, then how many possible values can q have?
- If and are the roots of the equation ax^2+bx+c=0, then which one of the following is correct?
- If the roots of the equation 4x^2-(5k+1)x+5k=0 differ by unity, then which one of the following is a possible value of k?
- What is the probability that the roots of the equation x^2+x+n=0 are real, where n N and n<4?
- Suppose a, b denote the distinct real roots of the quadratic polynomial x^2 + 20x - 2020 and suppose c, d denote the distinct...
- Let C_1 and C_2 be two biased coins such that the probabilities of getting head in a single toss are 2 3 and 1 3 , respectively....
- Let R ^2 denote R R . Let S = (a, b, c) : a, b, c R and ax^2 + 2bxy + cy^2 > 0 for all (x, y) R ^2 - (0, 0) . Then which of the...
- Let f(x) = x^4 + ax^3 + bx^2 + c be a polynomial with real coefficients such that f(1) = -9. Suppose that i 3 is a root of the...
- If , are the roots of the equation : x^ 2 - (5 + 3^ _ 3 5 - 3^ _ 5 3 ) + 3(3^ ( _ 3 5)^ 1/3 - 5^ ( _ 5 3)^ 2/3 - 1) = 0, then the...
- The number of functions f, from the set A = x N : x^ 2 - 10x + 9 0 to the set B = n^ 2 : n N such that f(x) (x - 3)^ 2 + 1, for...
- Let , be the roots of the equation x^ 2 - 4 x + 5 = 0 and , be the roots of the equation x^ 2 - (3 2 + 2 3 )x + 7 + 3 3 = 0, > 0....
- Let , be the roots of the equation x^ 2 - 2x + 6 = 0 and 1/ ^ 2 + 1, 1/ ^ 2 + 1 be the roots of the equation x^ 2 + ax + b = 0....
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