If α and β are the roots of the equation. 3x^2−6x+4=0, find the value of α^2+ β^2
Answers
Answered by
0
Answer:
Given Equation: 3x
2
−6x+4=0
We know that, Ifax
2
+bx+c=0 is a quadratic equation then root are x=
2a
−b±
b
2
−4ac
Substituting the values of a,b and c
x=
6
−6±
36−48
⇒α=
6
−6+
1
2i
&β=
6
−6−
1
2i
⇒α=
3
−3+
3
i
&β=
3
−3−
3
i
Finding α
2
+β
2
=(
3
−3+
3
i
)
2
+(
3
−3−
3
i
)
2
=
9
9−6
3
i−3
+
9
9+6
3
i−3
=
9
12
=
3
4
∴ The value of α
2
+β
2
=
3
4
Answered by
1
Answer:
ax2 + bx + c = 0, then
Sum of the roots = -(b/a)
Product of the roots = (c/a)
a2 + b2 = (a + b)2 – 2 × a × b
Calculation:
For equation, 3x2 – 7x + 2
a = 3, b = -7, and c = 2
Sum of the roots = -(b/a)
⇒ α + β = -(-7/3)
⇒ α + β = 7/3
Product of the roots = (c/a)
⇒ α × β = 2/3
Also, α2 + β2 = (α + β)2 – 2 × α × β
⇒ (7/3)2 – 2 × (2/3)
⇒ (49/9) – (4/3)
⇒ (49 – 12)/9
⇒ 37/9
∴ The value of α2 + β2 is 37/9.
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