If one root of the equation x^2+px+12=0 is 4, while the equation x^2+px+q=0 has equal roots, then the value of 'q' is - Mathematics MCQ AIEEE 2004 2004 | ExamTest.live

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If one root of the equation x^{2} + p x + 12 = 0 is 4, while the equation x^{2} + p x + q = 0 has equal roots, then the value of 'q' is

Solution & Step-by-step Explanation

Given that 4 is a root of x^{2} + p x + 12 = 0 : (4)^{2} + p (4) + 12 = 0 . 16 + 4 p + 12 = 0 28 + 4 p = 0 \Rightarrow p = - 7 . Now, for the equation x^{2} + p x + q = 0 to have equal roots, its discriminant must be zero (D = 0). D = p^{2} - 4 (1) (q) = 0 . Substituting p = - 7 : (- 7)^{2} - 4 q = 0 . 49 - 4 q = 0 q = \frac{49}{4} .

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If one root of the equation x^{2} + p x + 12 = 0 is 4, while the equation x^{2} + p x + q = 0 has equal roots, then the value of 'q' is

\frac{49}{4}

4

3

12

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