Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- Let and be the roots of the equation x^2+px+q=0. If ^3 and ^3 are the roots of the equation x^2+mx+n=0, then what is the value of...
- Let and be the roots of the equation x^2-ax-bx+ab-c=0. What is the quadratic equation whose roots are a and b?
- If the roots of the equation x^2-ax-bx-cx+bc+ca=0 are equal, then which one of the following is correct?
- Let and ( > ) be the roots of the equation x^2-8x+q=0. If ^2- ^2=16, then what is the value of q?
- For how many quadratic equations, the sum of roots is equal to the product of roots?
- Let p, q (p>q) be the roots of the quadratic equation x^2+bx+c=0 where c>0. If p^2+q^2-11pq=0, then what is p-q equal to?
- If 2-i 3 where i= -1 is a root of the equation x^2+ax+b=0, then what is the value of (a+b)?
- For how many integral values of k, the equation x^2-4x+k=0, where k is an integer has real roots and both of them lie in the...
- and are distinct real roots of the quadratic equation x^2+ax+b=0. Which of the following statements is/are sufficient to find ?...
- If - 2 and 3 are roots of the equation a_0+a_1x+a_2x^2+a_3x^3+x^4=0 where a_0, a_1, a_2, a_3 are integers, then which one of the...
- If a, b and c (a>0, c>0) are in GP, then consider the following in respect of the equation ax^2+bx+c=0 : 1. The equation has...
- Under which one of the following conditions does the equation ( -1)x^2+( )x+ =0 in x have a real root for [0, ]?
- If n is a root of the equation x^2+px+m=0 and m is a root of the equation x^2+px+n=0, where m n, then what is the value of p+m+n?
- The roots of the equation 7x^2-6x+1=0 are and , where 2 and 2 are the angles of a triangle. Which one of the following is correct?
- What is the number of real roots of the equation (x-1)^2+(x-3)^2+(x-5)^2=0?
- If one root of the equation x^2-kx+k=0 exceeds the other by 2 3 , then which one of the following is a value of k?
- If the highest degree coefficient is equal to 1, then what is the total number of quadratic equations which are unchanged on...
- Let and be the roots of the quadratic equation x^2-2bx+c^2=0 where b, c are positive real numbers. Let A be the arithmetic mean...
- Consider the following statements : I. x +x+1=0 has two irrational roots. II. 5 x -x-4=0 has two rational roots. Which of the...
- Let and be the roots of the equation x^2-p(x+1)-q=0 What is ^2+2 +1 ^2+2 +q + ^2+2 +1 ^2+2 +q equal to?
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