If the roots of a(b - c)x^2 + b(c - a)x + c(a | vedclass

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

Question

(C) The given quadratic equation is $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$.Since the roots are equal,the discriminant $D = 0$.Here,$A = a(b - c)$,$B

Vedclass · Accepted Answer

$H.P.$

Vedclass · Answer

(C) The given quadratic equation is $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$.Since the roots are equal,the discriminant $D = 0$.Here,$A = a(b - c)$,$B = b(c - a)$,and $C = c(a - b)$.$B^2 - 4AC = 0 \Rightarrow [b(c - a)]^2 - 4[a(b - c)][c(a - b)] = 0$.$b^2(c - a)^2 - 4ac(b - c)(a - b) = 0$.$b^2(c^2 - 2ac + a^2) - 4ac(ab - b^2 - ac + bc) = 0$.$b^2c^2 - 2ab^2c + a^2b^2 - 4a^2bc + 4ab^2c + 4a^2c^2 - 4abc^2 = 0$.$b^2c^2 + 2ab^2c + a^2b^2 - 4a^2bc - 4abc^2 + 4a^2c^2 = 0$.$(bc + ab - 2ac)^2 = 0$.$bc + ab = 2ac$.Dividing by $abc$,we get $\frac{1}{a} + \frac{1}{c} = \frac{2}{b}$.This implies that $a, b, c$ are in $H.P.$

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

Similar Questions

If the roots of the equation $6x^2 - 7x + k = 0$ are rational,then $k = .......$

In the real number system,the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has

The number of real roots of the equation $e^{4x} - e^{3x} - 4e^{2x} - e^{x} + 1 = 0$ is equal to $.....$

If one root of the equation $x^3-6x^2+3x+10=0$ is the average of the other two,then the sum of the fourth powers of the roots of the equation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module