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LAaMIpI UV, , Solve the equation x° — 19x” + 114 — 216 = 0 given that the roots, are'in G.P., Solution, , Let the roots be Be a, ap, , BZ % aB = 216; 0° = 216 or a=6, , , , 6 1 —i19 114 216, 0 6 7g 216, 1 13 36 0, , , , The other roots are given by, x — 1x + 36 =0, ie. x7 — Ox — 4x + 36 =0, (x - 9) -4)=0, ; x=9, x=4, .. The roots are 4, 6, 9., Example 7
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a:, , Solve the equation 6x? — 1Le? +6e —1=0 given that the roots are in HP, Solution |, , The roots of the equation 6x? — 11k? + @& —1=0 w (1)
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are in H.P., .. The roots of the equation P -— 6? + lix -—6=0 wun C2), are in H.P., Let the roots be a—-f,a,a+B, “a-Bt+tatat+B =6, , , , 3a =6 ora=2, . 2 is a root of the equation (2), 241 —6 1] —6, 0 2 —8 6, ] -4 3, . x -4x+3= 0, The other roots are given t (x-—1)(x-3)=0, x=1,2, Hence the roots of the €qUauvn (zy are 1, 2, 3., '. The roots of equation (1) are 1, e 7, , Example 15