Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If a,b,c are all positive and in H.P., then the roots of ax^2+2bx+c=0 are
- If c and d are roots of the equation (x-a)(x-b)-k=0, then a,b are roots of the equation
- If the equations x^2+px+q=0 and x^2+p'x+q'=0 have a common root, then it is equal to
- If , are the roots of ax^2+bx+c=0, the equation whose roots are 2+ , 2+ is
- If ax^2+bx-c is divisible by x^2+bx+c, then a' is a root of the equation
- If the roots of the equation ax^2-4x+a^2=0 are imaginary and the sum of the roots is equal to their product, then a=
- If , are the roots of x^2-3x+a=0, a R and <1< , then
- If and are the roots of x^2+px+1=0 and and are the roots of x^2+qx+1=0, then the value of ( - )( - )( + )( + ), is
- The graph of the function y=16x^2+8(a+5)x-7a-5 is strictly above the x-axis, then a' must satisfy the inequality
- The values of p for which the difference between the roots of the equation x^2+px+8=0 is 2, are
- Product of the real roots of the equation t^2x^2+|x|+9=0, (t 0)
- If the equation x^2+px+q=0 has roots u and v where p,q are non-zero constants. Then
- If the absolute value of the difference of the roots of the equation x^2+ax+1=0 exceeds 3a , then
- If p and q are roots of the quadratic equation x^2+mx+m^2+a=0, then the value of p^2+q^2+pq is
- If the equations k (6x^2+3 )+rx+2x^2-1=0 and 6k (2x^2+1 )+px+4x^2-2=0 have both roots common, then the value of (2r-p) is
- The value of k for which the equation 3x^2+2 (k^2+1 )x+k^2-3k+2=0 has roots of opposite signs, lies in the interval
- If x^2-2ra_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 x R, the least value of the expression x^2-6x+5 x^2+2x+1 , is
- The number of quadratic equations which are unchanged by squaring their roots is
- If x^2-bx ax-c = -1 +1 has roots equal in magnitude and opposite in sign then the value of is
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