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If α and 1/ α are the zeroes of the polynomial 4 – 2x + (k – 4 )find the value of k. |
Answer» QUESTION :If α and 1/ α are the zeroes of the polynomial 4x² – 2x + (k – 4 ) , find the value of k . Answér :k = 8 Note:★ The possible values of the VARIABLE for which the polynomial BECOMES zero are called its zeros . ★ A quadratic polynomial can have atmost two zeros . ★ The general form of a quadratic polynomial is given as ; ax² + bx + c . ★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ; • Sum of zeros , (α + ß) = -b/a • Product of zeros , (αß) = c/a Solution :The given quadratic polynomial is ; 4x² - 2x + (k - 4) . Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we have ; a = 4 b = -2 c = k - 4 Also , It is given that , α and 1/α are the zeros of the given quadratic polynomial . Thus , => Product of zeros = c/a => α × (1/α) = (k - 4)/4 => 1 = (k - 4)/4 => 1 × 4 = k - 4 => 4 = k - 4 => 4 + 4 = k => 8 = k => k = 8 Hence ,Required value of k is 8 . |
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