If a, b, c in Q,then the roots of the equatio | vedclass

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

Question

(A) Let the given quadratic equation be $Ax^2 + Bx + C = 0$,where $A = b + c - 2a$,$B = c + a - 2b$,and $C = a + b - 2c$.Sum of the coefficients is $A

Vedclass · Accepted Answer

Rational

Vedclass · Answer

(A) Let the given quadratic equation be $Ax^2 + Bx + C = 0$,where $A = b + c - 2a$,$B = c + a - 2b$,and $C = a + b - 2c$.Sum of the coefficients is $A + B + C = (b + c - 2a) + (c + a - 2b) + (a + b - 2c) = (a - a) + (b - b) + (c - c) = 0$.Since the sum of the coefficients is $0$,one root of the equation is $x = 1$.Since $a, b, c \in Q$,the coefficients $A, B, C$ are rational numbers.For a quadratic equation with rational coefficients,if one root is rational,the other root must also be rational (as the product of roots is $C/A$,which is rational).Therefore,the roots are rational.

List-$I$	List-$II$
$(i)$ $\alpha = \beta$	$(A)$ $(ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$
$(ii)$ $\alpha = 2\beta$	$(B)$ $2b^2 = 9ac$
$(iii)$ $\alpha = 3\beta$	$(C)$ $b^2 = 6ac$
$(iv)$ $\alpha = \beta^2$	$(D)$ $3b^2 = 16ac$
	$(E)$ $b^2 = 4ac$
	$(F)$ $(ac^2)^{1/3} + (a^2c)^{1/3} = b$

If $a, b, c \in Q$,then the roots of the equation $(b + c - 2a)x^2 + (c + a - 2b)x + (a + b - 2c) = 0$ are

Similar Questions

Each of the roots of the equation $x^3-6x^2+6x-5=0$ are increased by $h$. If the new transformed equation does not contain the $x^2$ term,then $h$ is equal to:

If the roots of the equation $x^2 - 2cx + ab = 0$ are real and unequal,then the roots of the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$ are

The equation having the multiple root of the equation $x^4+4x^3-16x-16=0$ as its root is

The condition that ${x^3} - 3px + 2q$ may be divisible by a factor of the form ${x^2} + 2ax + {a^2}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module