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51 The Quadratic Formula Find the two values, to 2 d.p., given by each of the following expressions: a) 2 ±2 b) 4 ± i10 3 0 —2 ±21/27 d) —3 -±142 3 e) —10±1160 5 —27±110 2 g) —8 ± V9.5 2.4 h) 10±188.4 23.2 The following quadratics can be solved by factorisation, but practise using the formula to solve them. a) x2 + 8x + 12 = 0 b) 6x2 — x — 2 = 0 c) x2— x — 6 = 0 d) x2 — 3x + 2 =0 e) 4x2 — 15x + 9 = 0 f) x2 — 3x = 0 g) 36x2 — 48x + 16 = 0 h) 3x2 + 8x = 0 1) 2x2 — 7x — 4 = 0 j) x2 + x — 20 = 0 k) 4x2 + 8x — 12 = 0 1) 3x2 — 11x — 20 = 0 m)x + 3 = 2x2 n) 5 — 3x — 2x2 = 0 o) 1 — 5x + 6x2 = 0 p) 3(x2 + 2x) = 9 q) x2 + 4(x — 3) = 0 r) x2 = 2(4 — x) ,\1',11 1)11;111111111 //i, _s= Step number 1... .1--:- -Write out the formula.E. N\011111,1111;! Step number 2... Write down values for a, b and c. iitt\' \\11 t11111111111111/111111// //// – Step number 3... sub a, b and c into the formula. Make sure – you divide the whole of the top line by 2a — not just 1/2 of it. – //// I //11111i111111111111111t 11\\ Solve the following quadratics using the formula. Give your answers to no more than two decimal places. a) x2 + 3x — 1 = 0 h) x2 + 4x + 2 = 0 b) x2 — 2x — 6 = 0 i) x2— 6x — 8 = 0 c) x2 + x — 1 =0 j) x2— 14x + 11 = 0 d) x2 + 6x + 3 = 0 k) x2 + 3x — 5 = 0 e) x2+ 5x + 2 =0 1) 7x2 — 15x + 6 = 0 0 x2— x — 1 =0 m) 2x2 + 6x — 3 =0 g) 3x2 + 10x — 8 = 0 n) 2x2 — 7x + 4 = 0 Oops, forgot to mention step number 4... check your answers by putting them back in the equation. SECTION THREE — ALGEBRA




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