Quadratic Equations Math Worksheet Page 12
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13Reinforcement Exercises (SPM Format Questions)
EXERCISE
EXERCISE
2
(a) The equation x
– 6x + 7 = h(2x – 3) has
L1
L2. One of the roots of the equation
2
roots which are equal. Find the values of h.
2x
+ 6x = 2k – 1 is twice the other. Find
[4]
the value of k and the roots of the equation.
(b) Given that α and β are roots of the equation
[1999]
2
x
– 2x + k = 0 , while 2α and 2β are the roots of
2
the equation x
+ mx + 9 = 0. Determine the
possible values of k and m.
[SPM 1999]
[6]
3
( x = -1 , x = -2 ; k =
)
9
( h = -1 , -2 ;
k =
2
4
L2. (SPM 2003 , P1, S3). Solve the quadratic
L3. (SPM 2003, P1, S4) The quadratic
equation 2x(x – 4) = (1 – x)(x + 2). Give your
equation x (x+1) = px – 4 has two distinct
answer correct to 4 significant sigures.
[3]
roots.. Find the range of values of p.
[3]
( x = 2.591, - 0.2573)
( p , -3 , p > 5)
L4
(SPM 2002) Find the range of k if the Q.E.
L5. (≈ SPM 2001) Show that the straight line
2
x
+ 3 = k (x – 1), k constant, has two distinct
y = 2 – x does not meet the curve
2
2
roots.
[3]
2x
– y
+ k = 0 if k > 8.
[3]
( k < -2 , k > 6)
2 Quadratic Equations
12
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