Find h

Algebra Level 2

(TIMO) If h is an integer, find the greatest value of h such that x 2 + ( h + 2 ) x + ( h + 5 ) = 0 x^{2} + (h+2)x + (h+5) = 0 has no real roots.


The answer is 3.

Ir J by IR J , 21, Philippines

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2 solutions

Lorenzo Aloe
Jul 28, 2018

T o h a v e 0 r e a l s o l u t i o n s w e m u s t h a v e Δ < 0 , t h e n ( h + 2 ) 2 − 4 ( h + 5 ) < 0. T h e n h 2 < 16 a n d − 4 < h < 4. T h e g r e a t e s t i s 3 To\ have\ 0\ real\ solutions\ we\ must\ have\ \Delta <0,\ then (h+2)^2-4(h+5)<0.\ Then\ h^2<16\ and -4<h<4.\ The\ greatest\ is\ \boxed{3}

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X X
Jul 28, 2018

Relevant wiki: Polynomial Roots

If it has no solution,then ( h + 2 ) 2 − 4 ( h + 5 ) < 0 , − 4 < 0 < 4 (h+2)^2-4(h+5)<0,-4<0<4 ,hence the answer is 3.

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