All the values of m for which both roots of t | vedclass

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

Question

(C) Given the quadratic equation $x^2 - 2mx + m^2 - 1 = 0$.This can be rewritten as $(x - m)^2 - 1 = 0$.Factoring the expression,we get $(x - m - 1)(x

Vedclass · Accepted Answer

$(-1, 3)$

Vedclass · Answer

(C) Given the quadratic equation $x^2 - 2mx + m^2 - 1 = 0$.This can be rewritten as $(x - m)^2 - 1 = 0$.Factoring the expression,we get $(x - m - 1)(x - m + 1) = 0$.Thus,the roots are $x_1 = m - 1$ and $x_2 = m + 1$.We are given that both roots must satisfy the condition $-2 For the smaller root $x_1 = m - 1$,we have $m - 1 > -2$,which implies $m > -1$.For the larger root $x_2 = m + 1$,we have $m + 1 Combining these inequalities,we get $-1 Therefore,the values of $m$ lie in the interval $(-1, 3)$.

All the values of $m$ for which both roots of the equation $x^2 - 2mx + m^2 - 1 = 0$ are greater than $-2$ but less than $4$ lie in the interval

Similar Questions

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} - 3481 = 0$
$II.$ $3y^{2} = \sqrt[3]{216000}$

If the product of the roots of the equation $(a + 1)x^2 + (2a + 3)x + (3a + 4) = 0$ is $2$,then the sum of the roots is:

The sum of the roots of the equation,${x^2} + |2x - 3| - 4 = 0$,is

Construct a quadratic equation whose roots have the sum $= 6$ and product $= -16$.

The quadratic equation in $t$,such that the Arithmetic Mean $(A.M.)$ of its roots is $A$ and the Geometric Mean $(G.M.)$ is $G$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module