Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- Let and be real numbers and z be a complex number. If z^2+ z+ =0 has two distinct non-real roots with Re (z)=1, then it is...
- What is the maximum value of 16 -12 ^2 ?
- If and ( 0) are the roots of the quadratic equation x^2+ x- =0, then the quadratic expression -x^2+ x+ where x R has
- Suppose f(x) is such a quadratic expression that it is positive for all real x. If g(x)=f(x)+f'(x)+f''(x), then for any real x
- If and (0< < < ) are the roots of the quadratic equation 4x^2-3=0, then what is the value of ?
- If A= ^2 + ^4 , then for all real , which one of the following is correct?
- The second degree equation x^2+4y^2-2x-4y+2=0 represents
- If both p and q belong to the set 1, 2, 3, 4 , then how many equations of the form px^2+qx+1=0 will have real roots?
- What is the value of k for which the sum of the squares of the roots of 2x^2-2(k-2)x-(k+1)=0 is minimum?
- If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, then which one of the following is correct?
- If |x^2-3x+2|>x^2-3x+2, then which one of the following is correct?
- Under which one of the following conditions will the quadratic equation x^2+mx+2=0 always have real roots?
- Let A B= x (x-a)(x-b)>0, where a<b . What are A and B equal to?
- How many real roots does the equation x^2+3|x|+2=0 have?
- Consider the following statements in respect of the quadratic equation 4(x-p)(x-q)-r^2=0, where p, q and r are real numbers : 1....
- Which one of the following is the second degree polynomial function f(x) where f(0)=5, f(-1)=10 and f(1)=6?
- If p and q are the roots of the equation x^2-30x+221=0, what is the value of p^3+q^3?
- If 1 5 x 4 5, then which one of the following is correct?
- The roots and of a quadratic equation, satisfy the relations + = ^2+ ^2 and = ^2 ^2. What is the number of such quadratic...
- If f(x)=3x^2-5x+p and f(0) and f(1) are opposite in sign, then which of the following is correct?
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