JAMB - Mathematics (1978 - No. 11)
If y = 2x2 + 9x - 35. Find the range of values for which y < 0.
7 < x < \(\frac{5}{2}\)
-5 < 7 < x
-7 < x < 5
-7 < x < \(\frac{5}{2}\)
Açıklama
y = 2x2 + 9x - 35
2x2 + 9x = 35
x2 + \(\frac{9}{2}\) = \(\frac{35}{2}\)
x2 + \(\frac{9}{2}\) + \(\frac{81}{16}\) = \(\frac{35}{2}\) = \(\frac{81}{16}\)
(x + \(\frac{9}{4}\))2 = \(\frac{361}{16}\)
x = \(\frac{-9}{4}\) + \(\frac{\sqrt{361}}{16}\)
x = \(\frac{-9}{4}\) + \(\frac{19}{4}\)
= 2.5 or -7
-7 < x < \(\frac{5}{2}\)
2x2 + 9x = 35
x2 + \(\frac{9}{2}\) = \(\frac{35}{2}\)
x2 + \(\frac{9}{2}\) + \(\frac{81}{16}\) = \(\frac{35}{2}\) = \(\frac{81}{16}\)
(x + \(\frac{9}{4}\))2 = \(\frac{361}{16}\)
x = \(\frac{-9}{4}\) + \(\frac{\sqrt{361}}{16}\)
x = \(\frac{-9}{4}\) + \(\frac{19}{4}\)
= 2.5 or -7
-7 < x < \(\frac{5}{2}\)