If the two equations x^2 - cx + d = 0 and x^2 | vedclass

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

Question

(C) Let the roots of $x^2 - cx + d = 0$ be $\alpha$ and $\beta$.Since the second equation $x^2 - ax + b = 0$ has equal roots and shares one common roo

Vedclass · Accepted Answer

$ac$

Vedclass · Answer

(C) Let the roots of $x^2 - cx + d = 0$ be $\alpha$ and $\beta$.Since the second equation $x^2 - ax + b = 0$ has equal roots and shares one common root $\alpha$ with the first,its roots must be $\alpha$ and $\alpha$.From the properties of roots:For the first equation: $\alpha + \beta = c$ and $\alpha \beta = d$.For the second equation: $\alpha + \alpha = a \implies 2\alpha = a$ and $\alpha^2 = b$.We need to find $2(b + d)$.Substituting the values: $2(b + d) = 2(\alpha^2 + \alpha \beta) = 2\alpha(\alpha + \beta)$.Since $2\alpha = a$ and $\alpha + \beta = c$,we get $2(b + d) = a 	imes c = ac$.

If the two equations $x^2 - cx + d = 0$ and $x^2 - ax + b = 0$ have one common root and the second equation has equal roots,then $2(b + d) = $

Similar Questions

If one of the roots of the equations $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ is common,then the numerical value of $(a + b)$ is

Let $\lambda \neq 0$ be in $\mathbb{R}$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+2\lambda=0$,and $\alpha$ and $\gamma$ are the roots of the equation $3x^{2}-10x+27\lambda=0$,then $\frac{\beta\gamma}{\lambda}$ is equal to:

The common roots of the equations $x^{12} - 1 = 0$ and $x^4 + x^2 + 1 = 0$ are:

If the equations $x^2 - cx + d = 0$ and $x^2 - ax + b = 0$ have one common root and the second equation has two equal roots,then $2(b + d) = \dots$

The value of $a$ for which the equations $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is

Vedclass Test Series

Exam Paper Generator

Online Exam Module