The roots of the equations 2x^2 - 5x + 1 = 0 | vedclass

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

Question

(B) Let the roots of the first equation $2x^2 - 5x + 1 = 0$ be $\alpha$ and $\beta$. Then,$\alpha \beta = \frac{c}{a} = \frac{1}{2}$. Now,consider the

Vedclass · Accepted Answer

Reciprocal and of opposite signs

Vedclass · Answer

(B) Let the roots of the first equation $2x^2 - 5x + 1 = 0$ be $\alpha$ and $\beta$. Then,$\alpha \beta = \frac{c}{a} = \frac{1}{2}$. Now,consider the second equation $x^2 + 5x + 2 = 0$. Let its roots be $\gamma$ and $\delta$. Then,$\gamma \delta = \frac{2}{1} = 2$. Comparing the two equations,we observe that the coefficients of the second equation are the reverse of the first,but with a sign change in the middle term. Specifically,if the roots of $ax^2 + bx + c = 0$ are $\alpha, \beta$,then the roots of $cx^2 + bx + a = 0$ are $\frac{1}{\alpha}, \frac{1}{\beta}$. For the equation $x^2 + 5x + 2 = 0$,which is $2x^2 + 5x + 1 = 0$ (if we consider the reciprocal property),the roots are related to the original. Actually,for $2x^2 - 5x + 1 = 0$,the roots are $\alpha, \beta$. For $x^2 + 5x + 2 = 0$,the roots are $-\frac{1}{\alpha}, -\frac{1}{\beta}$. Thus,the roots are reciprocals of each other and have opposite signs.

The roots of the equations $2x^2 - 5x + 1 = 0$ and $x^2 + 5x + 2 = 0$ are:

Similar Questions

If the roots of the equation $bx^2 + cx + a = 0$ are imaginary,then for all real values of $x$,the expression $3b^2x^2 + 6bcx + 2c^2$ is:

If $x^2-5x+6$ is a factor of $f(x)=x^4-17x^3+kx^2-247x+210$,then the other quadratic factor of $f(x)$ is

The sum of all distinct integral values of $\alpha$ such that the equation $x^2 - \alpha x + \alpha + 1 = 0$ has integral roots is equal to:

The number of roots of the equation $|x|^2 - 7|x| + 12 = 0$ is

Let $f(x) = Ax^2 + Bx$ and $g(x) = Lx^2 + Mx + N$. Given that $f(2) - g(2) = 1$, $f(3) - g(3) = 4$, and $f(4) - g(4) = 9$. Then a root of $f(x) - g(x) = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module