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

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

Question

(C) Given the quadratic equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$.Since the sum of the coefficients is $a(b - c) + b(c - a) + c(a - b) = ab -

Vedclass · Accepted Answer

$H.P.$

Vedclass · Answer

(C) Given the quadratic equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$.Since the sum of the coefficients is $a(b - c) + b(c - a) + c(a - b) = ab - ac + bc - ab + ac - bc = 0$,one root of the equation must be $1$.Since the roots are equal,both roots must be $1$.For a quadratic equation $Ax^2 + Bx + C = 0$,the product of roots is $\frac{C}{A}$.Thus,$1 	imes 1 = \frac{c(a - b)}{a(b - c)}$.$a(b - c) = c(a - b)$$ab - ac = ac - bc$$ab + bc = 2ac$Dividing both sides by $abc$,we get $\frac{1}{c} + \frac{1}{a} = \frac{2}{b}$.This implies that $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $A.P.$,which means $a, b, c$ are in $H.P.$

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

Similar Questions

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-Px^2+Qx-R=0$ and $(\alpha-2)^2, (\beta-2)^2, (\gamma-2)^2$ are the roots of the equation $x^3-5x^2+4x=0$,then the possible least value of $P+Q+R$ is

For how many values of $a$ does the equation $(a^2 - 3a + 2)x^2 + (a^2 - 4)x + a^2 - a - 2 = 0$ become a linear equation?

Consider two numbers whose arithmetic mean is $9$ and geometric mean is $4$. These numbers are the roots of which quadratic equation?

If ${x^2} + {y^2} = 25$ and ${xy} = 12$,then the possible values of $x$ are:

Let $p(x)$ be a quadratic polynomial such that $p(0) = 1$. If $p(x)$ leaves a remainder of $4$ when divided by $x - 1$ and a remainder of $6$ when divided by $x + 1$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module