If the difference between roots of the equation x2+ax+3=0 is less than √3 then sum of all the integral of x is equal to

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If the difference between roots of the equation x2+ax+3=0 is less than √3 then sum of all the integral of x is equal to

Asked by yadavashishkryadav | 13 Jan, 2023, 09:43: PM

Expert Answer

Let m and n be the roots of this quadratic equation where m>n

rightwards double arrow straight m minus straight n less than square root of 3 Now comma space straight m plus straight n equals negative straight a space and space mn equals 3 rightwards double arrow left parenthesis straight m plus straight n right parenthesis squared equals straight a squared space rightwards double arrow left parenthesis straight m minus straight n right parenthesis squared plus 4 mn equals straight a squared rightwards double arrow left parenthesis straight m minus straight n right parenthesis squared plus 12 equals straight a squared rightwards double arrow straight a squared equals left parenthesis straight m minus straight n right parenthesis squared plus 12 less than 3 plus 12 equals 15 rightwards double arrow straight a squared less than 15 rightwards double arrow straight a element of left parenthesis negative square root of 15 comma space square root of 15 right parenthesis

Answered by Renu Varma | 16 Jan, 2023, 11:28: AM

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