Question:
Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are :
Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are :
Updated On: Jul 15, 2023
- 44713
- 44654
- -6 , -1
- -4 , -3
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The Correct Option is A
Solution and Explanation
Let the correct equation be $ax^2 + bx + c = 0$
$-\frac{b}{a} = 7\quad\quad........ \left(i\right)$
$\frac{c}{a} = 6\quad\quad........ \left(ii\right)$
from $\left(i\right)$ and $\left(ii\right)$
correct equation is
$x^{2} - 7x + 6 = 0$
roots are 6 and 1
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Concepts Used:
Quadratic Equations
A polynomial that has two roots or is of degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b, and c are the real numbers.
Consider the following equation ax²+bx+c=0, where a≠0 and a, b, and c are real coefficients.
The solution of a quadratic equation can be found using the formula, x=((-b±√(b²-4ac))/2a)
Two important points to keep in mind are:
- A polynomial equation has at least one root.
- A polynomial equation of degree ‘n’ has ‘n’ roots.
Read More: Nature of Roots of Quadratic Equation
There are basically four methods of solving quadratic equations. They are:
- Factoring
- Completing the square
- Using Quadratic Formula
- Taking the square root