Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The number of integral values of a for which x^2-(a-1)x+3=0 has both roots positive and x^2+3x+6-a=0 has both roots negative is
- If X denotes the set of real numbers p for which the equation x^2=p(x+p) has its roots greater than p then X is equal to
- If ^4x+ ^2x-p=0, p R has real solutions then
- If one root of the equation (k^2+1)x^2+13x+4k=0 is reciprocal of the other then k has the value
- If the ratio of the roots of x^2+ x+ =0 is equal to the ratio of the roots of x^2+x+1=0 then , , are in
- If the roots of 4x^2+5k=(5k+1)x differ by unity then the negative value of k is
- If the product of the roots of the equation x^2-5x+4^ _2 =0 is 8 then is
- If , are the roots of x^2-px+q=0 then the product of the roots of the quadratic equation whose roots are ^2- ^2 and ^3- ^3 is
- If the sum of the roots of the quadratic equation ax^2+bx+c=0 is equal to the sum of the squares of their reciprocals then b^2 ac...
- If the absolute value of the difference of roots of the equation x^2+px+1=0 exceeds 3p then
- If , are roots of x^2+px+q=0 and , are the roots of x^2+px-r=0 then ( - )( - ) is equal to
- The quadratic equation whose roots are the AM and HM of the roots of the equation x^2+7x-1=0 is
- Let and ^2+3=5 while ^2=5 -3. The quadratic equation whose roots are and is
- If a and b are rational and b is not a perfect square then the quadratic equation with rational coefficients whose one root is 1...
- If 1 4-3i is a root of ax^2+bx+1=0, where a,b are real, then
- If , , be the roots of the equation x(1+x^2)+x^2(6+x)+2=0 then the value of ^ -1 + ^ -1 + ^ -1 is
- The roots of the equation x^3+14x^2-84x-216=0 are in
- If 3 and 1+ 2 are two roots of a cubic equation with rational coefficients then the equation is
- Let a,b,c be three real numbers such that 2a+3b+6c=0. Then the quadratic equation ax^2+bx+c=0 has
- The quadratic equations x^2+(a^2-2)x-2a^2=0 and x^2-3x+2=0 have
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