Question

If b = 0, c < 0, the roots of $ {x^2} + bx + c = 0 $ are numerically equal and opposite in sign.
A.True
B.False

Answer 1

Hint: In order to solve this question we will first let the negative number as the value of b is given to us in question is zero so we will put the negative value in place of constant and substitute to other side then we will find the nature of roots of this equation.

Complete step by step solution:
For solving this question we will first let a negative number to be –m so as it is given in question the equation is:
 $ {x^2} + bx + c = 0 $
As it is stated in question that the value of b is equals to zero and we will put the value of independent constant equal to –m in this equation so the new equation will be:
 $ {x^2} + 0x + \left( { - m} \right) = 0 $
Now on further solving this we will get:
 $ \Rightarrow {x^2} = m $
Now by taking the root on both side we will get the roots of x will be:
 $ \Rightarrow x = \pm \sqrt m $
So it is clear that the roots of this equation will be the same and of opposite signs so the statement will be true.
So the correct option will be A.
So, the correct answer is “Option A”.

Note: While solving these types of problems we should keep in mind that in question is already said that there is the independent term which is negative if it would have been given that the independent term is positive then the roots of the equation would have been imaginary.