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  • If b = 0, c < 0, is it true that the roots of x^{2 }+ bx+ c = 0 are numerically equal and opposite in sign? Justify.

If b = 0, c < 0, is it true that the roots of x2 + bx+ c = 0 are numerically equal and opposite in sign? Justify.

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True

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 \neq 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.

Let       c=-y

Put       b = 0, c = – y  in (2)
 \\x^{2}+0(x)-y=0\\ x^{2}=y\\ x=\pm \sqrt{y}\\ x=+\sqrt{y}\; \; \; \; \; \; \; \; \; \; x=-\sqrt{y}

Hence both the roots are equal and opposite in sign. Hence the given statement is true.

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