Question

if one of the roots of x² - 12x + k = 0 lies between 0 and 1 , then the range of k is (kindly give the solution)

​

Answer 1

Given:- roots of x² - 12x + k = 0 lies between 0 and 1.

To Find:- the range of k.

Answer :- As per Question , the roots of k lies between 0 and 1 . So the roots are greater than 0 , it means roots are real . For real roots we know that , Discriminant > 0 . And for a quadratic equation in standard form ax² + bx + c = 0 ; Discriminant is b² - 4ac .

=> b² - 4ac > 0

=> (-12)² - 4 × 1 × k > 0

=> 144 - 4k > 0

=> 144 > 4k.

=> 4k < 144

=> k < 144/4

=> k < 36 .

This implies k is less than 36 .

=> k € (-∞ , 36 )