Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The quadratic polynomial p(x) has the following properties: p(x) 0 for all real numbers, p(1)=0 and p(2)=2. Find the value of...
- If a and b are positive numbers and each of the equations x^2+ax+2b=0 and x^2+2bx+a=0 has real roots, then the smallest possible...
- Let P(x)=x^3-8x^2+cx-d be a polynomial with real coefficients and with all its roots being distinct positive integers. Then...
- If a^2-4a+1=4, then the value of a^3-a^2+a-1 a^2-1 (a^2 1 ) is equal to
- Let x^2+y^2+xy+1 a(x+y) x,y R, then the number of possible integer(s) in the range of a is
- The quadratic equation x^2+mx+n=0 has roots which are twice those of x^2+px+m=0 and m,n and p 0. Then the value n/p is
- If the equation x^2+2( +1)x+ ^2+ +7=0 has only negative roots, then the least value of equals
- If equation x^4-(3m+2)x^2+m^2=0 (m>0) has four real solutions which are in A.P., then the value of m' is
- All the values of k for which the quadratic polynomial f(x)=-2x^2+kx+k^2+5 has two distinct zeroes and only one of them...
- The number of integral solutions of x+2 x^2+1 > 12 is
- If 2-3x-2x^2 0, then
- The solution of 6+x-x^2>0, is
- The greatest negative integer satisfying x^2-4x-77<0 and x^2>4, is
- The number of integral solutions of 2(x+2)>x^2+1, is
- If x is an integer satisfying x^2-6x+5 0 and x^2-2x>0, then the number of positive values of x, is
- The set of all real values of x for which 8x^2+16x-51 (2x-3)(x+4) <3, is
- The number of integral solutions of x^2-3x-4<0, is
- The solution set of x^2+2 3x 2x^2-5, is
- The set of all integral values of x for which 5x-1<(x+1)^2<7x-3, is
- The set of real values of x for which 10x^2+17x-34 x^2+2x-3 <8, is
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