Exact set of values of a for which {x^3} | vedclass

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

Question

Equation becomes $4 a^{2}+6 a x-\left(x^{4}+x^{3}-2 x^{2}\right)=0$

$a=\frac{-6 x \pm \sqrt{36 x^{2}+16\left(x^{4}+x^{3}-2 x^{2}\right)}}{8}$

$a

Vedclass · Accepted Answer

$\left[ { - \frac{1}{8},\frac{1}{2}} \right]$

Vedclass · Answer

Equation becomes $4 a^{2}+6 a x-\left(x^{4}+x^{3}-2 x^{2}\right)=0$

$a=\frac{-6 x \pm \sqrt{36 x^{2}+16\left(x^{4}+x^{3}-2 x^{2}\right)}}{8}$

$a=\frac{-x^{2}}{2}-x$ and $a=\frac{x^{2}}{2}-\frac{x}{2}$

$\mathrm{x}^{2}+2 \mathrm{x}+2 \mathrm{a}=0$ or $\mathrm{x}^{2}-\mathrm{x}-2 \mathrm{a}=0$

$\mathrm{D}_{1} \geq 0$  and $ \mathrm{D}_{2} \geq 0$

$\mathrm{a} \in\left[-\frac{1}{8}, \frac{1}{2}\right]$

Exact set of values of $a$ for which ${x^3}(x + 1) = 2(x + a)(x + 2a)$ is having four real solutions is

Similar Questions

The number of solution$(s)$ of the equation $ln(lnx)$ = $log_xe$ is -

The number of solutions of the equation $\log _{(x+1)}\left(2 x^{2}+7 x+5\right)+\log _{(2 x+5)}(x+1)^{2}-4=0, x\,>\,0$, is $....$

Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is

Number of natural solutions of the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$ ) is equal to $n^2-10 n-36 ?$