If b = 0, c < 0, is it true that the roots of x2 + bx+ c = 0 are numerically equal and opposite in sign? Justify.
Quadratic Equation – A quadratic equation in x is an equation that can be written in the standard form, ax2 + bx + c = 0 Where a, b and c are real numbers with a 0
Roots : If ax2 + bx + c = 0 …..(1)
Is a quadratic equation then the values of x which satisfy equation 1 are the roots of the equation.
Here the given equation is x2 + bx+ c = 0 …..(2)
It is also given that b = 0, c < 0.
Put b = 0, c = – y in (2)
Hence both the roots are equal and opposite in sign. Hence the given statement is true.