Question

Anu and Aji solve an equation. In solving Anu commits a mistake in constant term and finds the roots 8 and 2. Aji commits a mistake in the coefficient of x. The correct roots are (a) 9,1 (b)-9,1 (c) 9, -1 (d) -9.-1​

Answer 1

The correct roots of the equation are (a) 9 and 1

From the complete question, their mistakes are:

Anu

• Roots: 8 and 2
• Wrong constant term

Aji

• Roots: -9 and -1
• Wrong coefficient

A quadratic equation is represented as:

$ax^2 + bx + c = 0$

Where:

$\alpha\beta = \frac ca$ --- product of roots

$\alpha + \beta = -\frac ba$ --- sum of roots

Anu made a mistake in the constant term, so we consider the sum of roots

$Sum = 8 + 2$

$Sum = 10$

Aji made a mistake in the coefficient, so we consider the product of roots

$Product = -9 \times -1$

$Product = 9$

The possible equations from the above sum and products are:

• $x^2 + 10x + 9 =0$.
• $x^2 - 10x + 9 =0$.
• $x^2 + 10x - 9 =0$.
• $x^2 - 10x - 9 =0$

Of all the above equations, the most likely equation is $x^2 - 10x + 9 =0$, and it has a root of 9 and 1

Hence, the correct roots are (a) 9 and 1

Read more about roots of equations at:

brainly.com/question/3923172