If both roots of the equation x^2 - 5ax + 6a | vedclass

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

Question

(A) Let $f(x) = x^2 - 5ax + 6a$. For both roots to be greater than $1$,the following conditions must be satisfied:$1$. Discriminant $D \ge 0$: $D = (-

Vedclass · Accepted Answer

$[\frac{24}{25}, \infty)$

Vedclass · Answer

(A) Let $f(x) = x^2 - 5ax + 6a$. For both roots to be greater than $1$,the following conditions must be satisfied:$1$. Discriminant $D \ge 0$: $D = (-5a)^2 - 4(1)(6a) = 25a^2 - 24a \ge 0 \implies a(25a - 24) \ge 0$. This gives $a \in (- \infty, 0] \cup [\frac{24}{25}, \infty)$.$2$. Vertex $x_v > 1$: $x_v = -\frac{b}{2a} = \frac{5a}{2} > 1 \implies a > \frac{2}{5}$.$3$. $f(1) > 0$: $f(1) = 1^2 - 5a(1) + 6a = 1 + a > 0 \implies a > -1$.Taking the intersection of all three conditions: $a \in (- \infty, 0] \cup [\frac{24}{25}, \infty)$ $AND$ $a > \frac{2}{5}$ $AND$ $a > -1$.The intersection is $a \in [\frac{24}{25}, \infty)$.

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed $1$,then the range of '$a$' is

Similar Questions

The equation $x^2 - 2xy + y^2 + 3x + 2 = 0$ represents:

Let $C$ be a curve $ax^2+2hxy+by^2+2gx+2fy+c=0$ in a Cartesian plane. By rotating the coordinate axes through an angle $\frac{\pi}{4}$ in the positive direction,if the transformed equation of $C$ is $Y^2+XY-X=0$,then $(h^2-ab)-2gf=$

The equation $x^2 + 4xy + y^2 + 2x + 4y + 2 = 0$ represents

The equation $16 x^2+y^2+8 x y-74 x-78 y+212=0$ represents

Which of the following equations does not represent a hyperbola?

Vedclass Test Series

Exam Paper Generator

Online Exam Module