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Sacred Heart of Mary Girls' School INEQUALITIES




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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. 2VBESBUicJOFRVBMJUZ
(2)

(b) Find the…

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Sacred Heart of Mary Girls' School INEQUALITIES




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8. The equation

x 2 + kx + 8 = k

has no real solutions for x.

(a) Show that k satisfies . 2VBESBUJDJOFRVBMJUZ
(3)

(b) Hence find the set of possible values of k.
(4)
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Sacred Heart of Mary Girls' School INEQUALITIES




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8. Given that the equation 2qx2 + qx ­ 1 = 0, where q is a constant, has no real roots,

(a) show that q2 + 8q < 0. 2VBESBUJDJOFRVBMJUZ
(2)

(b) Hence find the set of possible values…

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Sacred Heart of Mary Girls' School INEQUALITIES




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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. 2VBESBUJDJOFRVBMJUZ
(3)

(b)…

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4. Find the set of values of x for which

(a) 4x ­ 3 > 7 ­ x -JOFBSJOFRVBMJUZ
(2)

(b) 2x2 ­ 5x ­ 12 < 0 2VBESBUJDJOFRVBMJUZ
(4)

(c) both 4x ­ 3 > 7 ­ x and…

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3. Find the set of values of x for which

(a) 3(x ­ 2) < 8 ­ 2x -JOFBSJOFRVBMJUZ
(2)

(b) (2x ­ 7)(1 + x) < 0 2VBESBUJDJOFRVBMJUZ
(3)

(c) both 3(x ­ 2) < 8 ­ 2x and…

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