If alpha ,,beta ,,gamma are the roots of the | vedclass

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

Question

(c) If $\alpha, \beta , \gamma $ are the roots of the equation.

${x^3} - p{x^2} + qx - r = 0$

$	herefore {(\alpha + \beta )^{ - 1}} + {(\beta +

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(c) If $\alpha, \beta , \gamma $ are the roots of the equation.

${x^3} - p{x^2} + qx - r = 0$

$	herefore {(\alpha + \beta )^{ - 1}} + {(\beta + \gamma )^{ - 1}} + {(\gamma + \alpha )^{ - 1}} = \frac{{{p^2} + q}}{{pq - r}}$

Given, $p = 0,\,\,q = 4,\,\,\,r = - 1$

==> $\frac{{{p^2} + q}}{{pq - r}} = \frac{{0 + 4}}{{0 + 1}} = 4$.

If $\alpha ,\,\beta ,\,\gamma $ are the roots of the equation ${x^3} + 4x + 1 = 0,$ then ${(\alpha + \beta )^{ - 1}} + {(\beta + \gamma )^{ - 1}} + {(\gamma + \alpha )^{ - 1}} = $

Similar Questions

Let $A=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\right\}$ and $B=\{x \geq 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $n(A \cup B)$ is equal to:

If $a, b, c \in R$ and $1$ is a root of equation $ax^2 + bx + c = 0$, then the curve y $= 4ax^2 + 3bx+ 2c, a \ne 0$ intersect $x-$ axis at

If $\alpha, \beta $ and $\gamma$ are the roots of the equation $2{x^3} - 3{x^2} + 6x + 1 = 0$, then ${\alpha ^2} + {\beta ^2} + {\gamma ^2}$ is equal to

The number of solutions of $\sin ^2 \mathrm{x}+\left(2+2 \mathrm{x}-\mathrm{x}^2\right) \sin \mathrm{x}-3(\mathrm{x}-1)^2=0$, where $-\pi \leq \mathrm{x} \leq \pi$, is....................

Let $p(x)=a_0+a_1 x+\ldots+a_n x^n$ be a non-zero polynomial with integer coefficients. If $p(\sqrt{2}+\sqrt{3}+\sqrt{6})=0$, then the smallest possible value of $n$ is