Answer to Question #163842 in Algebra for Yolande

Question

19. c + 2x - 3x² is less than unity for all real values of x. the range of value of c is?

Answer 1

For quadratic expressions such as y=ax²+ bx+ c,

the maximum or minimum value of y=-(b² -4ac)/4a, where (b²-4ac) is the discriminant of the expression.

The discriminant of the polynomial is a quantity that determines the properties of the roots.

Thus, for this case, b²-4ac= (2)²- 4(-3)(c) = 4+12c

Since c+2x - 3x² < 1 for all real values of x,

then -(b²-4ac)/4a <1

-(4+12c)/4(-3) <1

(1/3) + c < 1

then the range of value of c is:

c< 2/3