Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If and are the roots of x^2-5x+16=0 and ^2+ ^2, 2 are the roots of x^2+ax+b=0, then find the value of a+b.
- Find the product of the roots of the equation 4^x-3 (2^ x+3 )+128=0.
- If one of the roots of the equation 6x^2+kx+6=0, k>0, is square of the other, then find the value of k.
- If and are the roots of x^2-5x+4=0, then find the value of ^3 2 cosec ^2 ( 12 ^ -1 )+ ^3 2 ^2 ( 12 ^ -1 ).
- Find the value of such that the sum of the squares of the roots of x^2+(4- )x+3= has the least value.
- If the roots of the equation 12x^2+mx+5=0 are in the ratio 3:2, then find the value of m^2.
- If the roots of the quadratic equation x^2-6x+ _2 =0 are real, then find the maximum value of .
- Find the largest integral value of m for which the quadratic expression y=x^2+(2m+4)x+7m+8 is positive for all x R.
- If one of the roots of the equation px^2-6x+q=0, where p and q are real numbers, is 32+ 72i, then find the value of |p-q|.
- Let z_1,z_2,z_3 be the roots of the equation x^3+bx^2+cx+d=0, b,c,d R. If z_1=1, z_2=1+Ai (A 0, A R), then evaluate d+c-b.
- Let , , be the three roots of the equation x^3+bx+c=0. If =1=- , then b^3+2c^3-3 ^3-6 ^3-8 ^3 is equal to
- Let for a a_1 0, f(x)=ax^2+bx+c, g(x)=a_1x^2+b_1x+c_1 and p(x)=f(x)-g(x). If p(x)=0 only for x=-1 and p(-2)=2, then the value of...
- Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in...
- If both the roots of the quadratic equation x^2-mx+4=0 are real and distinct and they lie in the interval [1,5] then m lies in...
- The number of all possible positive integral values of for which the roots of the quadratic equation, 6x^2-11x+ =0 are rational...
- Consider the quadratic equation (c-5)x^2-2cx+(c-4)=0, c 5. Let S be the set of all integral values of c for which one root of the...
- If one real root of the quadratic equation 81x^2+kx+256=0 is cube of the other root, then a value of k is
- Let and the roots of the quadratic equation x^2 -x( +1)+ =0 (0< <45^ ), and < . Then _ n=0 ^ ( ^n+ (-1)^n ^n ) is equal to
- If be the ratio of the roots of the quadratic equation in x, 3m^2x^2+m(m-4)x+2=0, then the least value of m for which + 1 =1, is
- The number of integral values of m for which the quadratic expression, (1+2m)x^2-2(1+3m)x+4(1+m), x R, is always positive, is
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