Question 15

Meera and Sarika attempted to solve a quadratic equation in x. Sarika made a mistake in reading the coefficient of x and obtained the roots as 12 and 16. Meera made a mistake in reading the constant term of the equation. She obtained the roots as-22 and - 6. The corrects root(s) is (are) :
(A) -16
(B) -12
(C) 12
(D) 16

Choose the correct answer from the options given below:

Solution

Let quadratic equation be $$x^2+bx+c\ =0$$
Now Sarika made a mistake in reading b , so she would have read c correctly
so c/1 = product of roots =192 (1)
Meera made a mistake in reading the constant term of the equation so she would have read b correctly
now sum of roots = -b/1 =-28 (2)
we get b =28 , c =192
so quadratic becomes
$$x^2+28x+192$$
we get (x+16)(x+12) =0
roots are -16 , -12

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