Maths-

General

Easy

Question

# Ramesh and Mahesh solve an equation. In solving Ramesh commits a mistake in constant term and finds the roots 8 and 2. Mahesh commits a mistake in the coefficient of x and finds the roots – 9 and – 1. The correct roots are

- – 8, 2
- 9, 1
- 9, - 1
- – 8, - 2

Hint:

### The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. With the use of the factorization approach, we will create two quadratic equations from two sets of roots found by Ramesh and Mahesh for a general quadratic equation.

## The correct answer is: 9, 1

### The quadratic equation has the following generic form ax² + bx + c = 0 where a, b, and c are numerical coefficients and x is an unknown variable. Here, an is greater than zero because if it equals zero, the equation will cease to be quadratic and change to a linear equation, such as bx+c=0.

A number is swiftly factorised into smaller numbers or factors of the number using the factorization formula. A factor is a number that evenly divides the inputted number. There are a maximum of n real roots that can exist for a polynomial of degree n.

Mahesh makes a mistake in the coefficient of x, and we learn that the roots of the equation are -9 and -1.

We will use factorization method to form a quadratic equation as we have roots of quadratic equation that are -9 and -1.

Then the quadratic equation will be:

(x−(−9))(x−(−1))=0

(x+9)(x+1)=0
⇒x^{2}+10x+9=0
Now comparing it with ax² + bx + c = 0, we get:
a=1,b=10,c=9
Now we have given that Mahesh commits a mistake in calculating the coefficient of x i.e. ‘b’ so b≠10 then a=1,c=9, then we get:
a=1,b=−10,c=9
Substitute the values of a, b and c in ax² + bx + c = 0, we get:
⇒−10x+9=0
−10x+9=0
Use the factorization method to find the roots of equation (4)

We can write equation (4) as

⇒−x−9x+9=0
Factorising it, we get:
( x − 1 ) ( x − 9 ) = 0 x = 1 and x = 9.

(x+9)(x+1)=0

^{2}+10x+9=0

Here we were given that in solving Ramesh commits a mistake in constant term and finds the roots 8 and 2. Many might create incorrect quadratic equations using the provided roots because they don't multiply carefully, which results in errors in one of the equation's signs. So the solution is 9, 1.

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