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| 1. |
Find the value of k,if the quadratic equation 3xsq - k√3x + 4=0 has real roots |
| Answer» \xa0If Discriminant of quadratic equation is equal to zero, or more than zero then roots are real.3x2 -k{tex}\\sqrt3{/tex}x + 4 = 0Compare with ax2 + bx + c = 0then a = 3, -k{tex}\\sqrt3{/tex}\xa0and c = 4D = b2- 4acFor real roots, b2- 4ac > 0{tex}( - k \\sqrt { 3 } ) ^ { 2 } - 4 \\times 3 \\times 4 \\geq 0{/tex}3k2- 48 {tex}\\geq{/tex}0k2\xa0- 16\xa0{tex}\\geq{/tex}0(k - 4)(k + 4) {tex}\\geq{/tex}\xa00{tex}\\therefore{/tex}\xa0k {tex}\\leq{/tex}\xa0- 4 and k{tex}\\geq{/tex}\xa04 | |