Question

Let x^ 2 -(m-3)x+m=0,(m in R) be quadratic equation. Match the following. List-I 1. Bothe roots are greater than 2 2. Bothe roots are smaller than 2 3. Exactly one root lies in (1,2) 4. Both roots lie in the interval (1,2) IV I 1) C 2) Ꭰ 3) C 4) C II D C D B III A A B D B B A A List-II A) m in(10, infty) B) m in phi C) m in[9,10) D) m in(- infty,1]​

Answer 1

Answer:

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Step-by-step explanation:

f(x)=x  

2

−(m−3)x+m=0

△=(m−3)  

2

−4m≥0  at least one root)

m  

2

−10m+9≥0

(,1]⋃[9)

For m<1, both roots are always <2

For example, m=0

x  

2

+3x,x=0,−3 (Both are <2)

∴For m ϵ[9] at least one root is greater than 2.