If α and β are the zeroes of the polynomial 2 xx 5 8 then the value of α + β is
If α and β are the zeros of the polynomial f(x) = kx2 + 4x + 4 such that α2 + β2 = 24, then find the positive value of k.
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Answer (Detailed Solution Below)Option 3 : \(\frac{2}{3}\) Free 100 Questions 100 Marks 60 Mins GIVEN: α and β are the Roots of the polynomial f(x) = kx2 + 4x + 4. α2 + β2 = 24 FORMULA USED: (a + b)2 = a2 + 2ab + b2 Sum of the roots (α + β) = - b / a and Product of roots (αβ) = c / a, where a = k, b = 4 and c = 4 SOLUTION: ⇒ α + β = - 4 / k ⇒ αβ = 4 / k ⇒ (α + β)2 = α2 + β2 + 2αβ ⇒ ( - 4 / k)2 = 24 + 8 / k ⇒ 16 / k2 = 24 + 8 / k ⇒ 16 / k2 - 8 / k = 24 ⇒ (16 - 8k) / k2 = 24 ⇒ 16 - 8k = 24 k2 ⇒ 24k2 + 8k - 16 = 0 ⇒ 3k2 + k - 2 = 0 ⇒ 3k2 + 3k - 2k - 2 = 0 ⇒ 3k × (k + 1) - 2(k + 1) = 0 ⇒ (3k - 2) × (k + 1) = 0 ⇒ (3k - 2) = 0 ⇒ k = 2 / 3 ⇒ (k + 1) = 0 ⇒ k = -1 Positive value of k = 2 / 3 Hence option 3 is the valid answer. Last updated on Sep 27, 2022 OPSC ASO Computer Skill Test Admit Card & List of Candidates Shortlisted Out on 1st December 2022. The skill test will be held on 4th December 2022. The Odisha Public Service Commission (OPSC) had released the OPSC ASO Result for the exam that was held on 27th August 2022. There is a 2-stage selection process for recruitment of OPSC ASO i.e. Online Written Test and Skill Test. Candidates who are qualified in the written test are eligible to attend the DV and Skill Test. A total vacancy of 796 were released for the recruitment. The Final Result will be released after the conclusion of Written Test and Skill Test. Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Algebra and ace the concept of Polynomials. Solution Since αandβ are zeroes of the given polynomial, we have Sum of roots (α+β)=−ba=−51=−5 option (b) -5 is correctSimilar questions Q. If α, β are zeroes of the polynomial f(x) = x2 + 5x + 8, then value of (α + β) is Q. If α and β are the zero of x2 + 5x + 8, then the value of (α + β) is (a) 5 Q. If α,β are zeros of
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α2(α2β−β)+β2(β2α−α) is View More Is alpha and beta are the zeros of the polynomial?alpha and beta are the zeros of a polynomial, such that alpha + beta = 6 and alphabeta = 4 .
Is alpha and beta are the zeros of polynomial x2 5x K?Given, that α, β are the zeroes of the polynomial f(x) = x2 – 5x + k. ∴ The value of k is 6.
What is the quadratic polynomial having zeros alpha and beta?∵α and β are zeroes of a polynomial. Hence, the quadratic polynomial is. x2−(α+β)x+α. β ⇒x2−(16+8)x+(16)(8)⇒x2−24x+128.
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