Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The roots of the equation |2x-1|^2-3|2x-1|+2=0 are
- Statement 1: If both roots of the equation 2x^2-x+a=0 (a R) lies in (1,2), then -1<a 18. Statement 2: If F(x)=2x^2-x+a, then D 0,...
- If each pair of the equation x^2+ax+b=0, x^2+bx+c=0 and x^2+cx+a=0 has a common root, then product of all common roots is
- Statement 1: If both roots of the equation 4x^2-2x+a=0, a R lie in the interval (-1,1), then -2<a 14. Statement 2: If...
- Number of integer roots of the equation (x+2)(x+3)(x+8)(x+12)=4x^2 is
- If the equation 2x^2+3x+5 =0 and x^2+2x+3 =0 have a common root, then is equal to
- If roots of x^2-ax+b=0 are prime numbers, then
- If the roots of the equation qx^2+px+q=0 are complex, where p,q are real, then the roots of the equation x^2-4qx+p^2=0 are
- If , are the roots of the quadratic equation ax^2+bx+c=0 and k be a real number, then the condition so that <k< is given by
- If and ( < ) are the roots of the equation x^2+bx+c=0 where c<0<b, then
- If the roots of the equation ax^2+bx+c=0 of the form k+1 k and k+2 k+1 , then (a+b+c)^2 is equal to
- The root of the equation 2(1+i)x^2-4(2-i)x-5-3i=0, where i= -1 , which has greater modulus, is
- If the roots of ax^2+bx+c=0 are , and the roots of Ax^2+Bx+C=0 are -k, -k, then B^2-4AC b^2-4ac is equal to
- If x_1,x_2,x_3 are distinct roots of the equation ax^2+bx+c=0, then
- The roots of the equation x^4-8x^2-9=0 are
- If , are the roots of x^2-ax+b=0 and if ^n+ ^n=V_n, then
- If b_1b_2=2 (c_1+c_2 ), then the least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has
- Let p,q 1,2,3,4 . The number of equations of the form px^2+qx+1=0 having real roots, is
- If x is real, the function (x-a)(x-b) (x-c) will assume all real values, provided
- Statement 1: If equations ax^2+bx+c=0, (a,b,c R) and 2x^2+3x+4=0 have a common root, then a:b:c=2:3:4. Statement 2: Roots of...
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