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12.3. Prove that the roots of the equation [tex]$(x-a)(x-b) = k^2$[/tex] are real for all values of [tex]$k$[/tex].
7. Show that the roots of the quadratic equation [tex]$(b-c) x^2 + 2(c-a) x + (a-b) = 0$[/tex] are real.
& Show that the roots of the equation [tex]$x^2 + (2m-1)x + m^2 = 0$[/tex] are real if [tex]$m \leq \frac{1}{4}$[/tex].
d. Show that the roots of the equation [tex]$x^2 + 4abx + \left(a^2 + 2b^2\right)^2 = 0$[/tex] are imaginary.
a. If the roots of the equation [tex]$qx^2 + 2px + 2q = 0$[/tex] are real and unequal, prove that the equation [tex]$(p+q)x^2 + 2qx + (p-q) = 0$[/tex] has imaginary roots.
Sagot :
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