FIND THE ROOTS OF
THE FOLLOWING
EQUATION ) 3x²-5x +2=0
Answers
Answer:
3x
²
−5x+2=0
Now divide the x
²
coefficient throughout,
⇒x
2
−
3
5x
+
3
2
Divide the coefficient of x by 2, and square it and add it and subtract it in the equation
⇒x
2
−
3
5x
+
3
2
+
36
25
−
36
25
=0
⇒x
2
−
3
5x
+
36
25
=
36
1
⇒
6
x−5
=±
6
1
6
x−5
=±
6
1
x=1 or
3
2
Step-by-step explanation:
\begin{aligned}3x^2+5x+2&=0\\[1em]&\downarrow\\[1em]\Delta&=5^2-(4\times3\times2)\\[1em]&=25-24\\[1em]&=\bold{1}\\[1em]&\downarrow\\[1em]x_1&=\frac{-5+\sqrt{1}}{2\times3}\\[1em]&=\frac{-5+1}{6}\\[1em]&=\frac{-4}{6}\\[1em]&=\bold{-0.66666667}\\[1em]&\downarrow\\[1em]x_2&=\frac{-5-\sqrt{1}}{2\times3}\\[1em]&=\frac{-5-1}{6}\\[1em]&=\frac{-6}{6}\\[1em]&=\bold{-1}\\[1em]\end{aligned}
3x
2
+5x+2
Δ
x
1
x
2
=0
↓
=5
2
−(4×3×2)
=25−24
=1
↓
=
2×3
−5+√
1
=
6
−5+1
=
6
−4
=−0.66666667
↓
=
2×3
−5−√
1
=
6
−5−1
=
6
−6
=−1