Question

if the two roots of the quadratic equation:4x-2x+m=0 belong to the interval]-1,1[,then
a)0<m<2
b)-2<m<0.75
c)-2<m≤0.25
d)2<m<2.5​

Answer 1

Answer:

pls make vote

Step-by-step explanation:

Question

Bookmark

If exactly one root of the quadratic equation x

2

−(a+1)x+2a=0 lies in the interval (0,3), then the set of values a is given by

Hard

Solution

verified

Verified by Toppr

Correct option is

B

(−∞,0]∪(6,∞)

For the equation x

2

−(a+1)x+2a=0 to have exactly one root lying between the interval (0,3), the following conditions should be satisfied,

(i)f(0)×f(3)<0

⇒(2a)(9−3(a+1)+2a)<0

⇒a(6−a)<0

⇒a(a−6)>0

⇒a<0 and a>6

(ii) Discriminant, D≥0

⇒(a+1)

2

−8a≥0

⇒a

2

−6a+1≥0

⇒(a−3)

2

−8≥0

⇒(a−(3+2

2

))(a−(3−2

2

))≥0

⇒a≥(3+2

2

) and a≤(3−2

2

)

The part of intersection for both of these conditions gives the set of values of a

i.e. a<0 and a>6

Also we have to check for the end points.

For a=0 we get the roots to be 0 and 1. Hence 0 is also possible. But for a=6 we get the roots to be 3 and 4, which does not lies in (0,3).

Hence, option 'B' is correct.