Question

Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are

Answer 1

GIVEN :

Mohan and Sohan solve an equation. In solving equation Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x and he find roots -9 and -1.

TO FIND :

The correct roots for the quadratic equation.

SOLUTION :

Given that Mohan and Sohan solve an equation

The standard form of quadratic equation is :

$ax^2+bx+c=0$ having roots as α and β

Now we have $sum of the roots=\alpha+\beta=-\frac{b}{a}$  

and $product of the roots=\alpha \beta=\frac{c}{a}$  

While solving Mohan commits a mistake in constant term and finds the roots 8 and 2.

Sum of the roots=8+2

=10

∴ Sum of the roots=10

And Sohan commits a mistake in the coefficient of x and he find roots -9 and -1.  

Product of roots=-9(-1)

=9

∴ Product of roots=9

The quadratic equation with roots is

$x^2-(sum of the roots)x+product of the roots=0$

Now the quadratic equation is  $x^2-10x+9=0$

$(x-9)(x-1)=0$

x-9=0 or x-1=0

∴  x= 9 and 1 are the roots of the quadratic equation  $x^2-10x+9=0$

∴  x= 9 and 1 are the correct roots.

Answer 2

Answer:

Correct sum = 8 + 2 = 10 from Mohan

Correct product = -9 x -1 = 9 from Sohan

∴ x² – (10)x + 9 = 0

⇒ x² – 10x + 9 = 0

⇒ x² – 9x – x + 9

⇒ x(x – 9) – 1(x – 9) = 0

⇒ (x-9) (x-l) = 0 .

⇒ Correct roots are 9 and 1