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If x^2 + 6x > 27, which of the following specifies all the possible values of x ?
A. x > 3
B. x < –9
C. –9 < x < 3
D. x > 3 or x < –9
E. x > 9 or x < –3
A. x > 3
B. x < –9
C. –9 < x < 3
D. x > 3 or x < –9
E. x > 9 or x < –3
05 Apr 2026, 22:17
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x^2+6x<27
x^2+6x-27<0
Factorize now
(x+9)(x-3)>0 ----- Eqn 1
Plot the critical points ie., 3,-9
When x>3 ; the above equation gives positive values.
When x<-9; the above equation gives positive values.
When -9<x<3 ; the above equation gives negative value.
We need to consider only positive values. therefore, x>3 and x<-9
Option D
x^2+6x-27<0
Factorize now
(x+9)(x-3)>0 ----- Eqn 1
Plot the critical points ie., 3,-9
When x>3 ; the above equation gives positive values.
When x<-9; the above equation gives positive values.
When -9<x<3 ; the above equation gives negative value.
We need to consider only positive values. therefore, x>3 and x<-9
Option D
05 Apr 2026, 23:55
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Taking 27 to the other side you get a quadratic with (x+9)(x-3)>0
This is a parabola opening upwards. For the values to be positive the values must be on either side of critical values.
The portion between -9 and 3 will be negative.
Remaining portion is fully positive.
Options D conveys just this.
This is a parabola opening upwards. For the values to be positive the values must be on either side of critical values.
The portion between -9 and 3 will be negative.
Remaining portion is fully positive.
Options D conveys just this.
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