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Check whether the equation 6x2 – 7x + 2 = 0 has real roots and if it has,find them by the method of factorisation.GIVE CORRECT ANSWERS ONLY |
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Answer» Answer: 6X2 – 7x + 2 = 0 has real ROOTS The roots are 2/3 and 1/2 Step-by-step explanation: If a quadratic equation has real roots then the discriminant (b² - 4ac ) is a positive value. The given quadratic equation be, 6x2 – 7x + 2 = 0 To find discriminant a = 6 , b = -7 and c = 2 b² - 4ac = (-7)² - (4*6*2) = 49 - 48 = 1 Therefore discriminant is positive, so he equation 6x2 – 7x + 2 = 0 has real roots Find the roots by the METHOD of COMPLETING the squares Let 6x2 – 7x + 2 = 0 ⇒ 6x2 – 7x = -2 ⇒x2 – 7x/6 = -2/6 Here b = -7/6 b/2 = -7/12 Adding both sides by (-7/12)² x2 – 7x/6 = -2/6 ⇒x2 – 7x/6 +(-7/12)² = -2/6 +(-7/12)² ⇒x2 – 7x/6 +(-7/12)² = -2/6 + 49/144 (x - 7/12)² = -48/144 + 49/144 (x - 7/12)² = 1/144 x - 7/12 = √( 1/144 ) x - 7/12 = ± 1/12 x = 1/12 + 7/12 or x = -1/12 + 7/12 x = 8/12 = 2/3 or x = 6/12 = 1/2 x = 2/3 or x = 1/2 Step-by-step explanation: |
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