Question

URGEENTT DAU CORONITA :o3
1) Rezolvati in R ecuatiile
a) x²+x-6-0
b) x²+x-12=0
2) Rezolvati in R ecuatiile :
a) 2x²+x-3=0
b) 2x-x-15=0
c) 3x-5x+12=0
d) 2x²-5x+2=0
e) 2x²-3x+1=0
f) 3x²-5x-3=0
AJUTATI-MA :o33

Answer 1

1.
a)x²+x-6=0
a=1
b=1
c=-6
Δ=b²-4ac
  =1²-4*1*(-6)
  =1+24
  =25>0
$x_{1,2}$=$\frac{-b+- \sqrt{Δ} }{2a}$=$\frac{-1+- \sqrt{25} }{2*1}= \frac{-1+-5}{2}$
$x_{1}$=$\frac{-1+5}{2}=2$
$x_{2}$=$\frac{-1-5}{2}= \frac{-6}{2}=-3$

b)x²+x-12=0
a=1
b=1
c=-12
Δ=b²-4ac
  =1²-4*1*(-12)
  =1+48
  =49>0
$x_{1,2}$=$\frac{-b+- \sqrt{Δ} }{2a}$=$\frac{-1+- \sqrt{49} }{2}= \frac{-1+-7}{2}$
$x_{1}$=[tex] \frac{-1+7}{2}= \frac{6}{2}=3 [/tex]
$x_{2}=\frac{-1-7}{2}= \frac{-8}{2}=-4$

2.
a)2x²+x-3=0
a=2
b=1
c=-3
Δ=b²-4ac
   =1²-4*2*(-3)
   =1+24
   =25>0
$x_{1,2}$=$\frac{-b+- \sqrt{Δ} }{2a}$=$\frac{-1+- \sqrt{25} }{2*2}= \frac{-1+-5}{4}$
$x_{1}= \frac{-1+5}{4}= \frac{4}{4}=1$
$x_{2}= \frac{-1-5}{4}= \frac{-6}{4}= \frac{-3}{2}$

b)  
2x²-x-15=0
a=2
b=1
c=-15
Δ=b²-4ac
  =1²-4*2*(-15)
  =1+120
  =121
$x_{1,2}$=$\frac{-b+- \sqrt{Δ} }{2a}$=$\frac{-1+-\sqrt{121} {2*2}= \frac{-1+ -11}{4}$
$x_{1}$=$\frac{-1+11}{4}= \frac{10}{4}= \frac{5}{2}$
$x_{2}= \frac{-1-11}{4}= \frac{-12}{4}=-3$

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

$x_{1,2}$=$\frac{-b+- \sqrt{Δ} }{2a}$=$\frac{5+- \sqrt{9} }{2*2}= \frac{5+-3}{4}$
$x_{1}= \frac{5+3}{4} \frac{8}{4}=2$
$x_{2}= \frac{5-3}{2}= \frac{2}{4}= \frac{1}{2}$

e)2x²-3x+1=0
a=2
b= -3
c=1
Δ=b²-4ac
  =(-3)²-4*2*1
  =9-8
  =1

$x_{1,2}$=$\frac{-b+- \sqrt{Δ} }{2a}$=$\frac{3+-1}{4}$
$x_{1}= \frac{3+1}{4}= \frac{4}{4}=1$
$x_{2}= \frac{3-1}{4}= \frac{2}{4}= \frac{1}{2}$