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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS June 2007
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7. The equation x 2 + kx + (k + 3) = 0 , where k is a constant, has different real roots.
(a) Show that k 2 - 4k - 12 > 0.
(2)
(b) Find the set of possible values of k.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS January 2008
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8. The equation
x 2 + kx + 8 = k
has no real solutions for x.
(a) Show that k satisfies .
(3)
(b) Hence find the set of possible values of k.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS January 2009
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7. The equation kx2 + 4x + (5 ­ k) = 0, where k is a constant, has 2 different real solutions
for x.
(a) Show that k satisfies
k2 ­ 5k + 4 > 0.
(3)
(b) Hence find the set of possible values of k.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS June 2009
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6. The equation x2 + 3px + p = 0, where p is a non-zero constant, has equal roots.
Find the value of p.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS January 2010
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10. f(x) = x 2 + 4kx + (3 + 11k ), where k is a constant.
(a) Express f(x) in the form ( x + p ) 2 + q, where p and q are constants to be found in terms
of k.
(3)
Given that the equation f(x) = 0 has no real roots,
(b) find the set of possible values of k.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS June 2010
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4. (a) Show that x 2 + 6 x + 11 can be written as
(x + p)2 +q
where p and q are integers to be found.
(2)
(b) In the space at the top of page 7, sketch the curve with equation y = x 2 + 6 x + 11,
showing clearly any intersections with the coordinate axes.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS January 2011
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8. The equation x 2 + (k - 3) x + (3 - 2k ) = 0, where k is a constant, has two distinct real
roots.
(a) Show that k satisfies
k 2 + 2k - 3 0
(3)
(b) Find the set of possible values of k.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS June 2011
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7. f ( x) = x 2 + (k + 3) x + k
where k is a real constant.
(a) Find the discriminant of f (x) in terms of k.
(2)
(b) Show that the discriminant of f (x) can be expressed in the form (k + a ) 2 + b, where
a and b are integers to be found.…read more

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Sacred Heart of Mary Girls' School QUADRATIC EQUATIONS January 2013
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9. The equation blank
( k + 3) x 2 + 6 x + k = 5 , where k is a constant,
has two distinct real solutions for x.
(a) Show that k satisfies
k 2 - 2k - 24 < 0
(4)
(b) Hence find the set of possible values of k.…read more

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