1.
a)x²+x-6=0
a=1
b=1
c=-6
Δ=b²-4ac
=1²-4*1*(-6)
=1+24
=25>0
[tex] x_{1,2} [/tex]=[tex] \frac{-b+- \sqrt{Δ} }{2a} [/tex]=[tex] \frac{-1+- \sqrt{25} }{2*1}= \frac{-1+-5}{2} [/tex]
[tex] x_{1} [/tex]=[tex] \frac{-1+5}{2}=2 [/tex]
[tex] x_{2} [/tex]=[tex] \frac{-1-5}{2}= \frac{-6}{2}=-3 [/tex]
b)x²+x-12=0
a=1
b=1
c=-12
Δ=b²-4ac
=1²-4*1*(-12)
=1+48
=49>0
[tex] x_{1,2} [/tex]=[tex] \frac{-b+- \sqrt{Δ} }{2a} [/tex]=[tex] \frac{-1+- \sqrt{49} }{2}= \frac{-1+-7}{2} [/tex]
[tex] x_{1} [/tex]=[tex] \frac{-1+7}{2}= \frac{6}{2}=3
[/tex]
[tex] x_{2}=\frac{-1-7}{2}= \frac{-8}{2}=-4 [/tex]
2.
a)2x²+x-3=0
a=2
b=1
c=-3
Δ=b²-4ac
=1²-4*2*(-3)
=1+24
=25>0
[tex] x_{1,2} [/tex]=[tex] \frac{-b+- \sqrt{Δ} }{2a} [/tex]=[tex] \frac{-1+- \sqrt{25} }{2*2}= \frac{-1+-5}{4}[/tex]
[tex] x_{1}= \frac{-1+5}{4}= \frac{4}{4}=1 [/tex]
[tex] x_{2}= \frac{-1-5}{4}= \frac{-6}{4}= \frac{-3}{2} [/tex]
b)
2x²-x-15=0
a=2
b=1
c=-15
Δ=b²-4ac
=1²-4*2*(-15)
=1+120
=121
[tex] x_{1,2} [/tex]=[tex] \frac{-b+- \sqrt{Δ} }{2a} [/tex]=[tex] \frac{-1+-\sqrt{121} {2*2}= \frac{-1+ -11}{4} [/tex]
[tex] x_{1} [/tex]=[tex] \frac{-1+11}{4}= \frac{10}{4}= \frac{5}{2} [/tex]
[tex] x_{2}= \frac{-1-11}{4}= \frac{-12}{4}=-3 [/tex]
c)3x²-5x+12=0
a=3
b=-5
c=12
Δ=b²-4ac
=(-5)²-4*3*12
=25-144
= -119<0=>
Ec. nu are solutii reale
d)2x²-5x+2=0
a=2
b= -5
c=2
Δ=b²-4ac
=(-5)²-4*2*2
=25-16
=9
[tex] x_{1,2} [/tex]=[tex] \frac{-b+- \sqrt{Δ} }{2a} [/tex]=[tex] \frac{5+- \sqrt{9} }{2*2}= \frac{5+-3}{4} [/tex]
[tex] x_{1}= \frac{5+3}{4} \frac{8}{4}=2 [/tex]
[tex] x_{2}= \frac{5-3}{2}= \frac{2}{4}= \frac{1}{2} [/tex]
e)2x²-3x+1=0
a=2
b= -3
c=1
Δ=b²-4ac
=(-3)²-4*2*1
=9-8
=1
[tex] x_{1,2} [/tex]=[tex] \frac{-b+- \sqrt{Δ} }{2a} [/tex]=[tex] \frac{3+-1}{4} [/tex]
[tex] x_{1}= \frac{3+1}{4}= \frac{4}{4}=1 [/tex]
[tex] x_{2}= \frac{3-1}{4}= \frac{2}{4}= \frac{1}{2} [/tex]
