Question

solve: 2xsquare+14x+9=0 where xis rational

Answer 1

2xsquare+14x=9=0
by applying -b+-root of b square -4ac whole divided by 4ac
-14+- root of 196- 4*2*9 whole divided by 4
=-14+-root of196-72 whole divided by 4
-14+-root of 124 whole divided by 4
-14+-2 root of 31 whole divided by 4
x=-7+root of 31 whole divided by 2 and another  x=-7-root of 31 divided by 2

Answer 2

2x² + 14x + 9 = 0

the roots are $\frac{-b+ \sqrt{ b^{2}-4ac } }{2a} and \frac{-b- \sqrt{ b^{2}-4ac } }{2a}$

$\frac{-14+ \sqrt{ 14^{2}-4*2*9 } }{2*2} and \frac{-14- \sqrt{ 14^{2}-4*2*9 } }{2*2}$

$\frac{-14+ \sqrt{ 196-72 } }{4} and \frac{-14- \sqrt{ 196-72 } }{4}$

$\frac{-14+ \sqrt{ 124 } }{4}and \frac{-14- \sqrt{ 124 } }{4}$

$\frac{-14+ 2\sqrt{ 31 } }{4}and \frac{-14- 2\sqrt{ 31 } }{4}$

$\frac{-7+ \sqrt{ 31 } }{2}and \frac{-7- \sqrt{ 31 } }{2}$

So both the roots are irrational. There are no rational roots.