Question

if α and β are the roots of the equation x²+3ax+2a²=0 and a²+β²=5 then value of a is?

Answer 1

Question:-

• If α and β are the roots of the equation x²+3ax+2a²=0 and α²+β²=5 then value of a is ?

Solution:-

Given ,

• Equation— x² + 3ax + 2a² = 0
• Roots → α and β
• α²+β² = 5

Since α and β are the roots of the above mentioned equation .

Therefore ,

• α + β = -3a/1 = -3a
• αβ = 2a²/1 = 2a²

We have ,

» α²+β² = 5

→ (α +β)² - 2αβ = 5 {rearranged}

→ (-3a)² - 2 × 2a² = 5

→ 9a² - 4a² = 5

→ 5a² = 5

→ a² = 5/5

→ a² = 1

→ a = ±√1

∴ a = ±1

Answer 2

Answer:

$a=\pm1$

Step-by-step explanation:

$\alpha \& \beta are two roots of the equation x^2+3ax+2a^2=0\\\\\therefore (x-\alpha)(x-\beta)=x^2+3ax+2a^2=0\\\implies x^2-(\alpha+\beta)x+\alpha\beta=x^2+3ax+2a^2\\\\ Comparing equivalent coefficient we get \\(\alpha+\beta)=-3a \& \alpha\beta=2a^2\\\\\alpha^2+\beta^2=5 (Given) \\\implies(\alpha+\beta)^{2}-2\alpha\beta=5\\\implies(-3a)^{2}-2\times2a^2=5\\\implies 9a^2-4a^2=5\\\implies 5a^2=5\\\implies a^2=1\\\implies a=\pm1$