persamaan kuadrat yang mempunyai akar real adalah (i) x²+3x-54=0 (ii) x²-8x+16=0 (iii) 2x²+5x+11=0 (iv) 3x²-7x+4=0 a. i, ii, dan iii b. i dan iii c. i dan ii d. i dan iv e. i, ii, dan iv

<p>Jawaban yang tepat adalah e. i, ii, dan iv</p><p>&nbsp;</p><p>Pembahasan :</p><ul><li>D &gt; 0, mempunyai 2 akar real yang berbeda</li><li>D = 0, Mempunyai 2 akar real yang sama (kembar)</li><li>D &lt; 0, mempunyai akar tidak real (imajiner)</li><li>Rumus D = b² - 4ac</li></ul><p>&nbsp;</p><p>(i) x² + 3x - 54 = 0</p><p>&nbsp; &nbsp; &nbsp;a = 1, b = 3, c = -54</p><p>&nbsp; &nbsp; &nbsp;D = 3² - 4(1)(-54)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 9 + 216</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 225</p><p>&nbsp; &nbsp; &nbsp; D &gt; 0, mempunyai 2 akar real yang berbeda</p><p>&nbsp;</p><p>(ii) x² - 8x + 16=0</p><p>&nbsp; &nbsp; &nbsp; a = 1, b = -8, c = 16</p><p>&nbsp; &nbsp; &nbsp; D = (-8)² - 4(1)(16)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 64 - 64</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp;D = 0, Mempunyai 2 akar real yang sama (kembar)</p><p>&nbsp;</p><p>(iii) 2x² + 5x + 11=0</p><p>&nbsp; &nbsp; &nbsp; &nbsp;a = 2, b = 5, c = 11</p><p>&nbsp; &nbsp; &nbsp; &nbsp;D = 5² - 4(2)(11)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 25 - 88</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= -63</p><p>&nbsp; &nbsp; &nbsp; &nbsp;D &lt; 0, mempunyai akar tidak real (imajiner)</p><p>&nbsp;</p><p>(iv) 3x² - 7x + 4 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp;a = 3, b = -7, c = 4</p><p>&nbsp; &nbsp; &nbsp; &nbsp;D = (-7)² - 4(3)(4)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 49 - 48</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 1</p><p>&nbsp; &nbsp; &nbsp; &nbsp;D &gt; 0, mempunyai 2 akar real yang berbeda</p>