The set of all real values of λ for which the quadratic equation λ 2 + 1 x 2 - 4 λ x + 2 = 0 always have exactly one root in the interval ( 0 ,   1 ) is :

Question

The set of all real values of &#955; for which the quadratic equation &#955; 2 + 1 x 2 - 4 &#955; x + 2 = 0 always have exactly one root in the interval ( 0 , &#160; 1 ) is :

Aicharya · Accepted Answer

f 0 &#183; f 1 &#8804; 0 &#8658; 2 &#955; 2 + 1 - 4 &#955; + 2 &#8804; 0 &#8658; 2 &#955; 2 - 4 &#955; + 3 &#8804; 0 &#8658; &#955; - 1 &#955; - 3 &#8804; 0 &#8658; &#955; &#8712; 1 , &#160; 3 But at &#955; = 1 , both roots are 1 . So, &#955; &#8800; 1

The set of all real values of λ for which the quadratic equation λ 2 + 1 x 2 - 4 λ x + 2 = 0…

Solution

The set of all real values of &#955; for which the quadratic equation &#955; 2 + 1 x 2 - 4 &#955; x + 2 = 0…

Solution

The set of all real values of λ for which the quadratic equation λ 2 + 1 x 2 - 4 λ x + 2 = 0…