Question

Find all values of 'm' such that the roots of the equation 2x^(2)-x-1=0 lie inside the roots of the equation x^(2)+(2m-m^(2))x-2m^(3)=0​

Answer 1

Answer:

your answer in given pic

Step-by-step explanation:

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Answer 2

m=-1/2 and 1

Explanation:

It is given that roots of the equation $2x^{2} -x-1=0$ lie inside the roots of the equation $x^{2} +(2m-m^{2})x-2m^{3}=0$ that means both roots are equal and discriminant of equation is 0.

$2x^{2} -x-1=0$

$2x^{2} -2x+x-1=0$

[tex]2x(x -1)+1(x-1)=0\\ [/tex]

$(2x+1)(x-1)=0$

Here we get x=-1/2 and 1

                                                                                                                                                                                                                                              Now we will put these values in equation  $x^{2} +(2m-m^{2})x-2m^{3}=0$

Put x= 1

$x^{2} +(2m-m^{2})x-2m^{3}=0$

$(1)^{2} +(2m-m^{2})(1) -2m^{3}=0$

 $2m^{3} +m^{2} -2m-1=0$

After solving we get,

m=-1/2 and m=1