Let the set of all values of p ∈ R , for which both the roots of the equation x 2 − ( p + 2 ) x + ( 2 p + 9 ) = 0 are negative real numbers, be the interval ( α , β ] . Then β − 2 α is equal to

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Using location of roots : (i) D ≥ 0 (ii) 2 a − b < 0 (iii) a. f ( 0 ) > 0 ( p + 2 ) 2 − 4 ( 2 p + 9 ) ≥ 0 ( p + 4 ) ( p − 8 ) ≥ 0 p + 2 < 0 2 p + 9 > 0 Intersection p ∈ ( − 2 9 , − 4 ] ∴ β − 2 α = − 4 + 9 = 5

Mathematics - Quadratic Equation Question with Solution | TestHub

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