Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If the equations x^2+ix+a=0, x^2-2x+ia=0, a 0 have a common root then
- If x^2-2r p_rx+r=0; r=1,2,3 are three quadratic equations of which each pair has exactly one root common then the number of...
- If ( ^2+ -2)x^2+( +2)x<1 for all x R then belongs to the interval
- The least integral value of k for which (k-2)x^2+8x+k+4>0 for all x R , is
- The set of possible values of x such that 5^x+(2 3)^ 2x -169 is always positive is
- If all real values of x obtained from the equation 4^x-(a-3)2^x+a-4=0 are nonpositive then
- The set of possible values of for which x^2-( ^2-5 +5)x+(2 ^2-3 -4)=0 has roots whose sum and product are both less than 1 is
- If ax^2+bx+6=0 does not have two distinct real roots, where a R , b R , then the least value of 3a+b is
- If x+ y-2 and x- y+1 are factors of the expression 6x^2-xy-y^2-6x+8y-12 then
- If a R , b R then the factors of the expression a(x^2-y^2)-bxy are
- The number of positive integral values of k for which (16x^2+12x+39)+k(9x^2-2x+11) is a perfect square is
- If x^2-bx+c=0 has equal integral roots then
- Let x^2-px+q=0, where p R , q R , have the roots , such that +2 =0 then
- If x^2+ax+b=0 and x^2+bx+a=0, a b, have a common root then
- If a, b, c are in GP, where a, c are positive, then the equation ax^2+bx+c=0 has
- If , are the roots of the equation x^2+x+3=0 then the equation 3x^2+5x+3=0 has a root
- If , are the roots of x^2-2ax+b^2=0 and , are the roots of x^2-2bx+a^2=0 then
- For the equation 2x^2+6 2 ,x+1=0
- If a, b, c are rational and no two of them are equal then the equations (b-c)x^2+(c-a)x+a-b=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0
- The equations x^2+b^2=1-2bx and x^2+a^2=1-2ax have one and only one root common. Then
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