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Find nature of root 3x2-√3+4=0 |
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Answer» Answer: For a quadratic EQUATION ax² + bx + c =0, the TERM b² - 4ac is called discriminant (D) of the quadratic equation because it determines whether the quadratic equation has real roots or not ( nature of roots). D= b² - 4ac So a quadratic equation ax² + bx + c =0, has i) Two distinct real roots, if b² - 4ac >0 , then x= -b/2a + √D/2a &x= -b/2a - √D/2a ii) Two EQUAL real roots, if b² - 4ac = 0 , then x= -b/2a or -b/2a iii) No real roots, if b² - 4ac <0 SOLUTION: Given: 3x² – 4√3x + 4 = 0 On Comparing it with ax² + bx + c = 0, we get a = 3, b = -4√3 and c = 4 Discriminant(D) = b² – 4ac D= (-4√3)² – 4(3)(4) D= 16 × 3 - 48 48 – 48 = 0 As , b² – 4ac = 0, Hence,the given quadratic equation has real and equal roots. HOPE THIS WILL HELP YOU ^_^
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