Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If px^2+qx+r=0 has no real roots and p, q, r are real such that p+r>0 then
- Let p and q be roots of the equation x^2-2x+A=0, and let r and s be the roots of the equation x^2-18x+B=0. If p<q<r<s are in...
- The quadratic equation x^2-2x- =0, 0,
- The graph of the curve x^2=3x-y-2 is
- a(x^2-y^2)+ x(y+1)+1 can be resolved into linear rational factors. Then
- If a, b are the real roots of x^2+px+1=0 and c, d are the real roots of x^2+qx+1=0 then (a-c)(b-c)(a+d)(b+d) is divisible by
- If x [2,4] then for the expression x^2-6x+5
- If 0<a<5, 0<b<5 and x^2+5 2 =x-2 (a+bx) is satisfied for at least one real x then the greatest value of a+b is
- If z_1,z_2,z_3,z_4 are roots of the equation a_0z^4+a_1z^3+a_2z^2+a_3z+a_4=0, where a_0,a_1,a_2,a_3 and a_4 are real, then
- The equation ( p-1)x^2+( p)x+ p=0 in x has real roots. Then the set of values of p is
- If =p, where |p| 1 then the quadratic equation whose roots are 2 and 2 is
- If x= , satisfies both the equations ^2x+a x+b=0 and ^2x+p x+q=0 then the relation between a,b,p and q is
- If 0 a 3, 0 b 3 and the equation x^2+4+3 (ax+b)=2x has at least one solution then the value of a+b is
- The equation =x+ px for all x R has a real solution for . Then
- The set of values of R such that ^2 + = holds for some is
- Let y= ^2x+ ^4x. Then for all real x
- If the equation a_1+a_2 2x+a_3 ^2x=1 is satisfied by every real value of x then the number of possible values of the triplet...
- If satisfies the inequation x^2 - x - 2 > 0 then a value exists for
- If , are roots of the equation 6x^2 + 11x + 3 = 0 then
- The set of values of k for which x^2-kx+ ^ -1 ( 4)>0 for all real x is
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