NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 4: Quadatric Equation - Exercise 4.2Question 7
Class 10 - Mathematics - CHAPTER 4: Quadatric Equation - Exercise 4.2
Question. 7
If b=0 and c<0, are the roots of \(x^2+bx+c=0\) numerically equal and opposite in sign? Justify.
Answer:
Yes.
Detailed Answer with Explanation:
Step 1: Start with the quadratic equation:
\(x^2 + bx + c = 0\)
Here, \(b = 0\). So the equation becomes:
\(x^2 + c = 0\)
Step 2: Rearrange the equation:
\(x^2 = -c\)
Step 3: We are told \(c < 0\) (c is negative). That means \(-c\) is positive.
So, \(-c = |c|\) (the absolute value of c).
Thus, \(x^2 = |c|\).
Step 4: Take the square root on both sides:
\(x = +\sqrt{|c|}\) or \(x = -\sqrt{|c|}\)
Step 5: These two roots have the same size (same numerical value) but one is positive and the other is negative.
That means they are equal in magnitude and opposite in sign.