Question
Question: If a Î [–20, 0] than the graph of the function y = 16x<sup>2</sup> + 8 (a + 5) x – 7a – 5 is strictl...
If a Î [–20, 0] than the graph of the function y = 16x2 + 8 (a + 5) x – 7a – 5 is strictly above the x-axis. How many Integral values of ‘a’ are possible –
A
12
B
11
C
13
D
None of these
Answer
13
Explanation
Solution
y = 16x2 + 8(a + 5) x – 7a – 5 > 0 " x
for above x-axis y > 0
̃ 16x2 + 8(a + 5) x – 7a – 5 > 0 " x
\ D < 0
̃ 64 (a + 5)2 – 4.16(7a – 5) < 0
̃ a2 + 17a + 30 < 0
(a + 15) (a + 2) < 0
̃ –15 < a < –2.
Total Integral value of a is 13.