2007-04-01 05:22:05 · 6 answers · asked by ree_na00 1 in Science & Mathematics ➔ Mathematics
Factorize the polynomial
4x^2 + 14x - 60 = 4(x^2 + 3.5x - 15) = 4(x^2 +2*1.75x + 1.75^2 -
- 1.75^2 - 15) = 3[(x + 1.75)^2 - 3.06255 - 15] =
= 4[(x + 1.75)^2 - 18.0625] =4[(x + 1.75)^2 - 4.25^2] =
= 4(x + 1.75 - 4.25)(x + 1.75 + 4.25) = 4(x + 6)(x - 2.5)
x1,2 = -6,2.5
If x< -6 then x+6 < -6 + 6 = 0
x - 2.5 < -6+2.5 = - 3.5 < 0
4x²+14x-60 = 4(x + 6)(x - 2.5) > 0
If -6 <= x <= 2.5
x + 6 <= -6 + 6 = 0
x-2.5 => +2.5 - 2.5 = 0
Hence, 4x²+14x-60 = 4(x + 6)(x - 2.5) <= 0
If x>2.5
x + 6 > 2.5 + 6 = 8.5 > 0
x - 2.5> 2.5 - 2.5 = 0
Hence, 4x²+14x-60 = 4(x + 6)(x - 2.5) >0
In order for the inequality to be true x must be in [-6, 2.5]
2007-04-01 05:38:17 · answer #1 · answered by Amit Y 5 · 0⤊ 1⤋
Hey there,
1) Simplify the equation by dividing it by 2, to make factorising easier.
4x^2 + 14x - 60 <= 0
2x^2 + 7x - 30 <= 0
2) Now factorise the equation.
(2x - 5)(x + 6) = 0
Therefore,
2x - 5 = 0
2x = 5
x = 5/2
x + 6 = 0
x = -6
**Check your answers by submitting x into your original equation.
[x = 5/2, -6]
(i) 4x^2 + 14x - 60
= 4(5/2)^2 + 14 (5/2) - 60
= 4 (25/4) + 35 - 60
= 25 + 35 - 60
= 0 (same as given equation)
(ii) 4x^2 + 14x - 60
= 4(-6)^2 + 14(-6) - 60
= 4(36) - 84 -60
= 144 - 144
= 0 (same as given equation)
Hope this helps! :)
2007-04-01 05:44:44 · answer #2 · answered by shopaholicstace 2 · 0⤊ 0⤋
4x²+14x-60<=0
(2x+12)(2x-5) <=0
2x+12<= 0 so x>= -6
2x-5 <= 0 so x<= 2.5
-6 <= x <= 2.5
2007-04-01 05:42:03 · answer #3 · answered by ironduke8159 7 · 1⤊ 0⤋
We can write this as (x-(5/2))(x-6)<=0.
Therefore x lies between 6 and (5/2) including the limits.
2007-04-01 05:30:54 · answer #4 · answered by L Srinath 1 · 0⤊ 1⤋
first divided by 2
u get 2x²+7x-30=0 factor it
(x-6) (2x+5)
x=6 ,or x= -5/2
2007-04-01 05:43:39 · answer #5 · answered by Khalidxp 3 · 0⤊ 0⤋
2x^2 +7x -30<= 0
(2x - 5)(x-6) <= 0
x=6,5/2
2007-04-01 05:30:47 · answer #6 · answered by John W 1 · 0⤊ 1⤋