Find the range of values x which satisfiesX2 – 4x < -3x2 – 4x + 3 < 0 [ In the form f(x) < 0 ](x - 1) (x – 3) < 0 [ factorise ]

From the graph above, the range of x which satisfies the inequality f(x) < 0 is 1 < x < 3 .

1) Find the range of values x which satisfies x2 – 5x + 6 < 0

2) Find the range of values x which satisfies (x+ 4) < 12 3) Find the range of values x which satisfies x2 + 2x < 0.

4) Find the range of values x which satisfies x2 + x - 6 ≥ 0

5) Find the range of values x which satisfies x2 + 3x - 10 ≥ 0.

6) Find the range of values x which satisfies 2x2 + x > 6. 7) Find the range of values x which satisfies x(4 – x) ≥ 0.

8) Find the range of x if x (x + 2) ≥ 15 9) State the range of x if 5x > 2 – 3x2.

10)Find the range of values x which satisfies 2x (x – 3) < 0

11)Find the range of x which satisfy the inequality (x – 1)2 > x – 1

12) Find the range of x if 3x (2x + 3) ≥ 4x + 1 13) Solve 5 + m2 > 9 – 3m.

14) Solve -2x (x + 3) > 0 15) Find the range of x if 9x2 > 4.

16) Find the range of value of x for which 17) Find the range of values of x for which

18) Find the range of values of x for which 19) Given that , find the range of value of x.

Show that the function 2x – 3 – x2 is alwaysnegative for all values of x.Ans : Let f(x) = 2x – 3 – x2= - x2 + 2x - 3a = -1, b = 2, c = -3b2 – 4ac = 22 – 4(-1)(-3)= 4 - 12< 0Since a < 0 and b2 – 4ac < 0, the graph y = f(x) always lies above the x-axis f(x) is always negative for all x.

1) Show that the function 4x – 2x2 – 5 is always negative for all values of x.

2) Show that the function 2x2 – 3x + 2 is always positive for all values of x.

3) Show that the curve y = 9 + 4x2 – 12x touches the x-axis.

4) Find the range of p if the graph of the quadratic function f(x) = 2x2 + x + 5 + p cuts the x-axis at TWO different points.

5) Find the range of p if the graph of quadratic function f(x) = x2 + px – 2p cuts the x-axis at TWO different points.

6) The graph of the function f(x) = 2x2 + (3 – k)x + 8 does not touch the x axis. Determine the range of k.

7) Find the values of k if the graph of the quadratic function y = x2 + 2kx + k + 6 touches the x-axis.

8) Given that the quadratic equation has roots, find the range of value

m.

9) Find the range of values of q for which has roots

10) Show that is always negative for all values of x.

11) Given that has no roots, find the range of values of k.

12) Given that the line and the curve show that the line do not meet if