Quadratic and Simultaneous Equations

1.4 Quadratic and Simultaneous Equations – Problems

1. Use factorisation to solve the following quadratic Equations:

[pic 1] x x2   12 0[pic 2]

[pic 3]

[pic 4]

1. [pic 5]x2   7 10 0x        [pic 6]        [pic 7]

[pic 8]

[pic 9]

1. x2   5 6 0x        [pic 10]

[pic 11]

1. x x2  6[pic 12][pic 13][pic 14]

[pic 15]

1. x2  4 5x        [pic 16][pic 18][pic 17]

        [f] x2  6x        9[pic 19]

[pic 20]

1. Use factorisation to solve the following quadratic Equations:

        [pic 21]2x2   3 2 0x        [pic 22] [pic 23]

[pic 24]

[pic 25]

        [b]3x2 10 8 0x         [pic 26] [pic 27]        [pic 28]        [pic 29]        [pic 30]        [c]2x2   7 15 0x        [pic 31][pic 32]

        [pic 33]                                              [pic 34] 

        [d]2x2  5 7x        [pic 35] [pic 36]        [pic 37]        [pic 38]        [pic 39]        [pic 40]        [pic 41][pic 42]

        [pic 43]                                               

        [e]15x2   3 18 0x        [pic 44]

[pic 45]

[pic 46]

        [f]7x2   6 1 0x        [pic 47]

[pic 48]

[pic 49]

1. Use factorisation to solve the following quadratic Equations: (Here we have the case when c=0 in the form ax2 bxc0).

1. x2 16 0x [pic 50]        [pic 51][pic 52]

[pic 53]

[pic 54]

1. x2  7 0x        [pic 55]        [pic 56]        [pic 57]        [pic 58]        [pic 59]        [c] x2  3 0x        [pic 60][pic 61]

        [d]2x x2  0        [pic 62]        [pic 63]        [pic 64]        [pic 65]        [pic 66]        [e] x2  4 0x        [pic 67]        [pic 68][pic 69]

        [f]5x2  6 0x        [pic 70]

[pic 71]

1. Use factorisation to solve the following quadratic Equations:

[pic 72] x2  25 0[pic 73]

[pic 74]

[pic 75]

        [b]4x2  16 0        [pic 76]        [pic 77]        [pic 78]        [pic 79]        [c]2x2  32 0[pic 80][pic 81]

1. Solve the following quadratic Equations without factorisation: (Here we have the case when b=0 in the form ax2 bxc0):

1. [pic 82]x2  25 0[pic 83]        [pic 84]

[pic 85]

[pic 86]

        [b]4x2  16 0[pic 87]        [pic 88]        [pic 89]        [pic 90]        [pic 91]        [pic 92][pic 93]

[c]2x2  32 0[pic 94]

[pic 95]

1. Solve the following quadratic equations using the formula and giving your answer to 2 decimal places:

1. 2x2   11 5 0x        [pic 96] [pic 97][pic 98]

[pic 99]

[pic 100]

[pic 101]

        [b]5x2   7 2 0x        [pic 102]        [pic 103]        [pic 104]        [pic 105]        [c]2x2   7 15 0x        [pic 106][pic 107]

[pic 108]

        [d]2 x 6x2 0        [pic 109]        [pic 110]        [pic 111]        [pic 112]        [pic 113][pic 114]

        [f]2x2   5 1 0x        [pic 115]

[pic 116]

7. By considering the quantity (b2 4ac) in the quadratic formula, determine whether each of the following quadratics have real solutions:

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