First slide

Theory of equations

Question

$The roots of a x^{2} + 2 b x + c = 0 and b x^{2} - 2 \sqrt{a c} x + b = 0 are simultaneously real then$

Moderate

A

$a c = b^{2}$
B

$4 b^{2} = a c$
C

$a = b, c = 0$
D

None of these

Solution

$\begin{array}{l} D_{1} \geq 0, D_{2} \geq 0 \\ \Rightarrow b^{2} - a c \geq 0, a c - b^{2} \geq 0 \\ \Rightarrow b^{2} - a c = 0 \end{array}$

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