Let f(x)=ax2+bx+c,a=0. Then the discriminant if f(x) is
D=b2−4acThe equation f(x)=6x−18 has exactly one root
ax2+bx+c=6x−18
ax2+(b−6)x+(c+18)=0
(b−6)2−4a(c+18)=0 The equation f(x)=9−3x has exactly one root
ax2+bx+c=9−3x
ax2+(b+3)x+(c−9)=0
(b+3)2−4a(c−9)=0
We have the system
b2−12b+36−4ac−72a=0b2+6b+9−4ac+36a=0
b2−4ac=12b+72a−36b2−4ac=−6b−36a−9
12b+72a−36=−6b−36a−9
b=−6a+1.5b2−4ac=36a−9−36a−9
D=−18
The value of the discriminant of f(x) is −18.
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