Question

The number of solutions for 9x^2 - 30x + 37 = 9sin2x ?

Answer 1

@hartnn @satellite73 @RadEn

Answer 2

graph em
they don't intersect

Answer 3

http://www.wolframalpha.com/input/?i=9x%5E2+-+30x+%2B+37+%3D+9sin2x


Have a look at this.

Answer 4

Is there any way to find it manually i mean...With out Graph...:)

Answer 5

yes there is a way to find the number of real solution of given equation:::
step1:
let y=9x^2 - 30x + 37
step2:
and let y=9sin2x
step 3:
plot the graph of both equation in the same axis ..
step 4:
the point of intersection of the both curve will give the number of real solution of the given equation..

Answer 6

Complete the square on the left hand side. What is the minimum value of that expression?

Answer 7

that wont quite do it

Answer 8

oh yes it will, sorry

Answer 9

y=9x^2 - 30x + 37 this is the eqn of parabola so draw the graph of this parabola.
and y=9sin2x is a sine curve which maximum value will be 9 and minimum value will be -9 .and also draw it.

Answer 10

@tkhunny has a method without the graph
min is too large,

Answer 11

but this will not work in general, because it could be that the min value of the parabola is less that the max of the sine curve, but they still could not intersect

Answer 12

True. I thought it might be a good first clue.

Answer 13

\[12\le9x ^{2}-30x+37\]
and
\[-9 \le \sin 2x \le 9\]
wee see that te two curve will never intersect to each other

Answer 14

@Taufique typo. "9*" missing from the sine expression.

Answer 15

ohh sorry ..yes ,9 is missing in the above equation