Quadratic EquationHard
Question
Let $a,b$, are real numbers such that $a + b = 5$. Then the equation $x^{2} - ax - b = 0$ must have for all real values of a
Options
A.equal real roots
B.imaginary roots
C.distinct real roots
D.nothing can be said
Solution
$f(x) = x^{2} - ax - b$
and
$$\begin{matrix} f(1) & \ = 1 - a - b = - 4 \\ x & \ \rightarrow \pm \infty,f(x) \rightarrow \infty \end{matrix}$$
$\Rightarrow f(x) = 0$ has two distinct real roots.
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
The number of points in (- ∞,∞), for which x2 - xsinx - cosx = 0, is...x1 and x2 are the roots of equation ax2 + bx + c = 0 (Where a, b, c ∈ R) and x1x2 < 0, then roots of the equati...The largest interval for which x12 - x9 + x4 - x +1 > 0 is...If α, β are roots of the equation (3x + 2)2 + p ( 3x + 2) + q = 0, then roots of x2 + px + q = 0 are -...If the equation = 1 has roots equal in magnitude but opposite in sign, then the value of a + b is -...