Let f(x) = x^2 + 2bx + 2c^2 and g(x) = -x^2 - | vedclass

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

Question

(C) The minimum value of $f(x) = x^2 + 2bx + 2c^2$ is found at $x = -b$,which is $f(-b) = (-b)^2 + 2b(-b) + 2c^2 = b^2 - 2b^2 + 2c^2 = 2c^2 - b^2$.The

Vedclass · Accepted Answer

$(\sqrt{2}, \infty)$

Vedclass · Answer

(C) The minimum value of $f(x) = x^2 + 2bx + 2c^2$ is found at $x = -b$,which is $f(-b) = (-b)^2 + 2b(-b) + 2c^2 = b^2 - 2b^2 + 2c^2 = 2c^2 - b^2$.The maximum value of $g(x) = -x^2 - 2cx + b^2$ is found at $x = -c$,which is $g(-c) = -(-c)^2 - 2c(-c) + b^2 = -c^2 + 2c^2 + b^2 = c^2 + b^2$.Given $\min f(x) > \max g(x)$,we have $2c^2 - b^2 > c^2 + b^2$.This simplifies to $c^2 > 2b^2$,or $\frac{c^2}{b^2} > 2$.Taking the square root of both sides,we get $\left|\frac{c}{b}\right| > \sqrt{2}$.Thus,$\left|\frac{c}{b}\right| \in (\sqrt{2}, \infty)$.

Quadratic expression	The minimum value
i) $x^2 + 4x + 6$	a) $1$
ii) $x^2 - 2x + 5$	b) $2$
iii) $x^2 + 6x + 18$	c) $4$
iv) $x^2 - 4x + 5$	d) $9$

Let $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = -x^2 - 2cx + b^2$,where $x \in R$. If $b$ and $c$ are nonzero real numbers such that $\min f(x) > \max g(x)$,then $\left|\frac{c}{b}\right|$ lies in the interval:

Similar Questions

If $\alpha, \beta$ are the roots of $x^2+bx+c=0$,$\gamma, \delta$ are the roots of $x^2+b_1x+c_1=0$ and $\gamma < \alpha < \delta < \beta$,then $(c-c_1)^2 < $

The value of $p$ for which both the roots of the equation $4x^2 - 20px + (25p^2 + 15p - 66) = 0$ are less than $2$ lies in:

The number of integral values of $k$,for which one root of the equation $2x^2-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$,is:

The set of values of $a$ such that $x^2 - 2ax + a^2 - 6a \leqslant 0$ for all $x \in [1, 2]$ is

Match the following quadratic expressions with their minimum values:
Quadratic expression The minimum value
i) $x^2 + 4x + 6$ a) $1$
ii) $x^2 - 2x + 5$ b) $2$
iii) $x^2 + 6x + 18$ c) $4$
iv) $x^2 - 4x + 5$ d) $9$

Vedclass Test Series

Exam Paper Generator

Online Exam Module