Handle these Quadratic Inequalities!

Algebra Level 4

If all the solutions of the inequality x 2 + 6 a x + 5 a 2 ≤ 0 { x }^{ 2 }+6ax+5{ a }^{ 2 }\quad \le \quad 0 are also the solutions of the inequality x 2 − 14 x + 40 ≤ 0 { x }^{ 2 }-14x+40\quad \le \quad 0 , find the number of integral values of 'a'.


The answer is 0.

Ninad Akolekar by Ninad Akolekar , 23, India

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1 solution

Parveen Soni
Nov 9, 2014

sum of roots=-6a=14 ------>No integral value
product of roots=5a^2=40----------->No integral value.

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