If a, b, c are distinct real numbers and a^3 | vedclass

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

Question

(B) Given the identity $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) = 0$.This can be written as $\frac{1}{2}(a + b + c)[(a -

Vedclass · Accepted Answer

$\frac{c}{a}$

Vedclass · Answer

(B) Given the identity $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) = 0$.This can be written as $\frac{1}{2}(a + b + c)[(a - b)^2 + (b - c)^2 + (c - a)^2] = 0$.Since $a, b, c$ are distinct,$(a - b)^2 + (b - c)^2 + (c - a)^2 
eq 0$.Therefore,we must have $a + b + c = 0$.For the quadratic equation $ax^2 + bx + c = 0$,if we substitute $x = 1$,we get $a(1)^2 + b(1) + c = a + b + c$.Since $a + b + c = 0$,$x = 1$ is one root of the equation.Let the roots be $\alpha$ and $\beta$. We know $\alpha \cdot \beta = \frac{c}{a}$.Since $\alpha = 1$,the other root $\beta = \frac{c}{a}$.

If $a, b, c$ are distinct real numbers and $a^3 + b^3 + c^3 = 3abc$,then the equation $ax^2 + bx + c = 0$ has two roots,out of which one root is

Similar Questions

If $x$ is real,then the minimum value of $y = \frac{x^2-x+1}{x^2+x+1}$ is

If $f(x) \in \mathbb{Q}[x]$ is a non-zero polynomial such that all its roots are irrational,then the degree of $f(x)$ is

If both roots of the equation $x^2 - (p - 4)x + 2e^{2 \ln p} - 4 = 0$ are negative,then in which interval does $p$ lie?

$A$ building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the work in: (in $days$)

Let $x = (\sqrt{50} + 7)^{1/3} - (\sqrt{50} - 7)^{1/3}$. Then,

Vedclass Test Series

Exam Paper Generator

Online Exam Module