Grade 12Algebra

the number of integral solutions of alpha for which for which the above question is valid

chaitanya

8 Years agoGrade 12

8 Years ago

Dear student,

the graph of quadratic should be downward because if the graph is upward it can be positive for infinite value of negative integers so

$\alpha$ $\alpha$ -3 is always $\alpha$

so the given equation becomes

$\alpha$ x²+(3-2 $\alpha$ )x-6 factorizes into (x-2)( $\alpha$ x+3)

roots are 2,-3/ $\alpha$
exactly 2 integers are present in between roots so 1 and 0 or 3 and 4

case 1: 1 and 0 are the integers

so -3/ $\alpha$ $\alpha$ >0 but $\alpha$

case 2: 3 and 4 are the integers

so -3/ $\alpha$ > 4 : $\alpha$ >-3/4 and $\alpha$ $\alpha$ is integer so the possible values of $\alpha$ are none

finally o possible values of $\alpha$

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