Sachin and Rahul solve a quadratic equation. | vedclass

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

Question

(B) Let the quadratic equation be $x^2 + bx + c = 0$.Sachin made a mistake in the constant term $c$,so his roots $(4, 3)$ are correct for the coeffici

Vedclass · Accepted Answer

$6, 1$

Vedclass · Answer

(B) Let the quadratic equation be $x^2 + bx + c = 0$.Sachin made a mistake in the constant term $c$,so his roots $(4, 3)$ are correct for the coefficient $b$. The sum of roots is $-(b) = 4 + 3 = 7$,so $b = -7$.Rahul made a mistake in the coefficient $b$,so his roots $(3, 2)$ are correct for the constant term $c$. The product of roots is $c = 3 	imes 2 = 6$.The correct quadratic equation is $x^2 - 7x + 6 = 0$.Factoring the equation: $x^2 - 6x - x + 6 = 0 \implies x(x - 6) - 1(x - 6) = 0 \implies (x - 6)(x - 1) = 0$.The correct roots are $x = 6$ and $x = 1$.

Sachin and Rahul solve a quadratic equation. Sachin makes a mistake in writing the constant term and obtains roots $(4, 3)$. Rahul makes a mistake in writing the coefficient of $x$ and obtains roots $(3, 2)$. What are the correct roots of the equation?

Similar Questions

Consider the two equations $x^2 - 2ax + b^2 = 0$ and $x^2 - 2bx + a^2 = 0$. The arithmetic mean of the roots of the first equation is equal to what?

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda)x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

Let $\alpha$ and $\beta$ be the roots of $x^{2}-6x-2=0$. If $a_{n}=\alpha^{n}-\beta^{n}$ for $n \geq 1$,then the value of $\frac{a_{10}-2a_{8}}{3a_{9}}$ is ..... .

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$ ($a \ne 0$; $a, b, c$ being distinct),then $(1 + \alpha + \alpha^2)(1 + \beta + \beta^2) = $

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module