Question

One of the two students, while solving a quadratic
equation in x , copied the constant term incorrectly
and got the roots 3 and 2. The other copied the
constant term and coefficient of x2
correctly as −6
and 1 respectively. The correct roots are

Answer 1

Answer:

here is your answer

correct roots are

x=3 and x= -2

Answer 2

The correct roots of the quadratic equation are 6 and - 1 .

• Let the given quadratic equation be ax² + bx + c = 0.

Here, x represents the roots of the equation.

Coefficient of x² = a

Coefficient of x = b

Constant term = c

• Given,

Incorrect roots of the equation = 3, 2

=> x = 3  ;  x = 2.

=> x - 3 = 0 -(i)  ;  x - 2 = 0  -(ii)

• A quadratic equation is formed by multiplying the linear equations (i) and (ii).

=> (x - 3) (x - 2) = 0 × 0

=> (x - 3) (x - 2) = 0

=> x² - 2x - 3x + 6 = 0

=> x² - 5x + 6 = 0

•  Given that the correct value of the coefficient of x² = 1

=> a = 1

Correct value of the constant term = - 6

=> c = - 6

• It is given that the first student copies only the value of the constant term incorrectly.

=> The coefficient of x is copied correctly by the first student.

=> b = - 5

• Now, putting the values of a, b, and c in the quadratic equation correctly, we get,

1.x² + (- 5).x + (- 6) = 0

=> x² - 5x - 6 = 0

=> x² - 6x + x - 6 = 0

=> x (x - 6) + 1 (x - 6) = 0

=> (x - 6) (x + 1) = 0

=> x - 6 = 0  ;  x + 1 = 0

=> x = 6  ;  x = - 1

• Therefore, the correct roots of the given quadratic equation are 6 and - 1 .