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if 2 is the root of quadratic equation 3xsquare+px-p=0and quadratic equation 4xsquare-2px+k=0 has equal roots find k |
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Answer» <P>Step-by-step explanation: 2 is the root of quadratic equation 3x² + px - 8 = 0………….(1) & 4x² - 2px + k = 0 has equal roots ………….(2) On putting the value of given root i.e X = 2 in eq 1 . 3x² + px - 8 = 0 3(2)² + p(2) − 8 = 0 3 × 4 + 2P - 8 = 0 12 + 2p − 8 = 0 4 + 2p = 0 2p = - 4 p = - 4/ 2 = -2 p = - 2 Hence the value of p is - 2. On putting the value of p = - 2 in eq 2, 4x² - 2px + k = 0 4x² - 2(- 2)x + k = 0 4x² + 4x + k = 0 On comparing the given equation with ax² + bx + c = 0 Here, a = 4, b = 4 , and c = k D(discriminant) = b² – 4ac Given : Quadratic equation has equal roots i.e D = 0 b² – 4ac = 0 4² – 4(4)(k) = 0 16 – 16k = 0 16 = 16k k = 16/16 = 1 k = 1 Hence, the value of k is 1 . ★★ NATURE OF THE ROOTS If D = 0 roots are real and equal If D > 0 roots are real and distinct If D < 0 No real roots Read more on Brainly.in - brainly.in/question/2427512#readmore |
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