Get 2 FREE Instant-Explanations on Filo with code FILOAPP

If , , are the roots of the equation 2x^3-3x^2+6x+1=0, then ^

Question

If $α, β, γ$ are the roots of the equation $2 x^{3} - 3 x^{2} + 6 x + 1 = 0$ , then $α^{2} + β^{2} + γ^{2}$ is equal to

- \frac{15}{4}

\frac{15}{4}

\frac{9}{4}

4

Views: 960 students

Found 5 tutors discussing this question

Sophia Discussed

α, β, γ

are the roots of the equation

2 x^{3} - 3 x^{2} + 6 x + 1 = 0

, then

α^{2} + β^{2} + γ^{2}

is equal to

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given equation

2 x^{3} - 3 x^{2} + 6 x + 1 = 0

,
Sum of roots:

α + β + γ = \frac{3}{2}

Product of roots:

α β γ = \frac{- 1}{2}

Sum of roots taken

2

at a time:

Σ α β = \frac{6}{2} = 3

Now, we know that

(α + β + γ)^{2} = α^{2} + β^{2} + γ^{2} + 2 (α β + β γ + γ α)

Re-arranging, we get

α^{2} + β^{2} + γ^{2} = (α + β + γ)^{2} - 2 (Σ α β)

α^{2} + β^{2} + γ^{2} = (\frac{3}{2})^{2} - 2 \times 3 = \frac{9}{4} - 6 = - \frac{15}{4}

Hence, option A.

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	If $α, β, γ$ are the roots of the equation $2 x^{3} - 3 x^{2} + 6 x + 1 = 0$ , then $α^{2} + β^{2} + γ^{2}$ is equal to
Answer Type	Text solution:1
Upvotes	150