Question

If α, β are the roots of 4x2 - 16x +c=0 c>0 such that.1<α<2<B<3, then the number of integral values of 'c' is​

Answer 1

Answer:

The Answer is Seven(7)

Explanation:

The sum of the roots of a quadratic equation is c/a where a is the coefficient of x2

Here in the equation sum of the roots (Alpha + Beta) = C/4

Here 1 < (Alpha) < 2

2 < (Beta) < 3

Adding the both equations...

We get , 3 < (Alpha + Beta ) < 5

Now we get 3< C/4 < 5..

Multiply with 4 on both sides.

Then we get [ 12< C < 20 ]

The integers between 12 and 20 are

(13,14,15,16,17,18,19)

No.of integral values = 7

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