If the roots of {x^2} + x + a = 0exceed a, th | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(d) If the roots of the quadratic equation $a{x^2} + bx + c = 0$ exceed a number k, then $a{k^2} + bk + c > 0$ if $a > 0,$ ${b^2} - 4ac \ge 0$ a

Vedclass · Accepted Answer

$a < - 2$

Vedclass · Answer

(d) If the roots of the quadratic equation $a{x^2} + bx + c = 0$ exceed a number k, then $a{k^2} + bk + c > 0$ if $a > 0,$ ${b^2} - 4ac \ge 0$ and sum of the roots $ > 2k$ Therefore, if the roots of ${x^2} + x + a = 0$ exceed a number a, then ${a^2} + a + a > 0,1 - 4a \ge 0$ and $ - 1 > 2a$ ==> $a(a + 2) > 0,$$a \le \frac{1}{4}$and $a < - \frac{1}{2}$ ==> $a > 0\,{\rm{or}}\,a < - 2,a < \frac{1}{4}$and $a < - \frac{1}{2}$ Hence $a < - 2$.

If the roots of ${x^2} + x + a = 0$exceed $a$, then

Similar Questions

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{{x + 2}}{{x - 1}} < 4,$ is

The number of integers $k$ for which the equation $x^3-27 x+k=0$ has at least two distinct integer roots is

The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations $x+y^2=x^2+y=12$ is

The number of pairs of reals $(x, y)$ such that $x=x^2+y^2$ and $y=2 x y$ is

If $x$ be real, the least value of ${x^2} - 6x + 10$ is