In writing a quadratic equation of the form `x^(2) + px + q = 0`,a student makes a mistake in writing the coefficientof x and gets the roots as 8 and 12. Another student makes mistake in writing the constant term and gets the roots as 7 and 3. Find the correct quadratic equation.

Options

A. `x^(2) + 10x + 96 = 0`
B. `x^(2) - 20x + 21 = 0`
C. `x^(2) - 21x + 20 = 0`
D. `x^(2) - 96x + 10 = 0`

Answer

A

Explanation

(i) Use the concept of sum and product of the roots of a quadratic equation.
(ii) The product of the roots obtained by the first student is product of the roots of the required quadratic equation.
(iii) The sum of the roots obtained by the secon student of the roots of the required qua-dratic equation.