What is the quadratic polynomial whose sum and the product of zeros is root 2 half respectively?
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Sum of the zeroes = -3/2√5x Show
Product of the zeroes = – ½ P(x) = x2 – (sum of the zeroes) + (product of the zeroes) Then, P(x)= x2 -3/2√5x – ½ P(x)= 2√5x2 – 3x – √5 Using splitting the middle term method, 2√5x2 – 3x – √5 = 0 2√5x2 – (5x – 2x) – √5 = 0 2√5x2 – 5x + 2x – √5 = 0 √5x (2x – √5) – (2x – √5) = 0 (2x – √5)(√5 – 1) = 0 ⇒ x = – 1/√5, √5/2 Mẹo về What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? Mới NhấtBùi Đình Hùng đang tìm kiếm từ khóa What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? được Update vào lúc : 2022-10-04 14:10:48 . Với phương châm chia sẻ Kinh Nghiệm Hướng dẫn trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi đọc tài liệu vẫn ko hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Ad lý giải và hướng dẫn lại nha. Free Nội dung chính
Bihar Police Fireman Full Mock Test 2022 100 Questions 100 Marks 120 Mins Given: The sum of roots = -3 The product of roots = 2 Concept used: The sum of roots of quadratic equation = -b/a The product of roots = c/a Calculation: The quadratic polynomial is in the form of P(x) = ax2 + bx + c According to the question Sum of roots = -3 ⇒ -b/a = -3 Product of roots = 2 ⇒ c/a = 2 ⇒ a = 1, b = 3 and c = 2 The quadratic polynomial wiil be P(x) = x2 + 3x + 2 ∴ The required quadratic polynomial is x2 + 3x + 2. Latest Bihar Police Fireman Updates Last updated on Sep 26, 2022 The Central Selection Board of Constables (CSBC) has released the Bihar Police Fireman Result for the written examination that was conducted on 27th March 2022 and 28th August 2022. The result is out for Advt No. 01/2022. The qualified candidates for the written examination will go for the next round which is the Physical Efficiency Test (PET). The PET round will be conducted in the month of November 2022. The candidates for the post of Bihar Police Fireman will get a salary range between Rs. 21,700 to Rs. 69,100. Let's discuss the concepts related to Algebra and Quadratic Equation. Explore more from Quantitative Aptitude here. Learn now! Solution Step 1: Solve for equation of the quadratic polynomialGiven,Sum of zeros =-83Product of zeros=43We know that, the equation of the quadratic polynomial can be written as,x2-(sum of zeros)+(product of zeros)=0∴x2--83x+4 3=0⇒3x2+8x+ 4=0Step 2: Factorize the polynomial3x2+8x+4=0⇒x3x+2+23x +2=0⇒x+23x +2=0⇒ x=-2,-23Hence, the zeroes of the given polynomial are -2,-23This answer was edited. The General form of a quadratic polynomial whose Sum of roots and products of roots is given : x2- ( Sum of roots) x + ( Product of roots ) =0 In the above question, Now, The quadratic polynomial Required polynomial is 3x²−3√2x+1 Solution: Given, the sum of two zeros are 2. Product of two zeros is -3/2. We have to find the quadratic polynomial and its zeros. A quadratic polynomial in terms of the zeroes (α,β) is given by x2 - (sum of the zeroes) x + (product of the zeroes) i.e, f(x) = x2 -(α +β) x +αβ Here, sum of the roots, α +β = √2 Product of the roots, αβ = 3/2 So, the quadratic polynomial can be written as x² - √2x - 3/2. The polynomial can be rewritten as (1/2)[2x² - 2√2x - 3]. On factoring the polynomial, 2x² + √2x - 3√2x - 3 = 0 √2x(√2x + 1) - 3(√2x + 1) = 0 (√2x - 3)(√2x + 1) = 0 Now, √2x - 3 = 0 √2x = 3 x = 3/√2 Also, √2x + 1 = 0 √2x = -1 x = -1/√2 Therefore, the zeros of the polynomial are -1/√2 and 3/√2 ✦ Try This: Find a quadratic polynomial, the sum and product of whose zeroes are 2 and 3/2, respectively. Also find its zeroes ☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2 NCERT Exemplar Class 10 Maths Exercise 2.4 Solved Problem 1 Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2, respectively. Also find its zeroesSummary: A quadratic polynomial whose sum and product of zeroes are √2 and 3/2 is x² - √2x + 3/2= 0. The zeros of the polynomial are -1/√2 and 3/√2 ☛ Related Questions:
Sum of zeroes = α + β =√2 Product of zeroes = α β = 1/3 ∴ If α and β are zeroes of any quadratic polynomial, then the quadratic polynomial equation can be written directly as:- x2–(α+β)x +αβ = 0 x2 –(√2)x + (1/3) = 0 3x2-3√2x+1 = 0 Thus, 3x2-3√2x+1 is the quadratic polynomial. What is the quadratic polynomial whose sum and product of zeroes is √ 2 1 3 respectively?NCERT Solutions Class 10 Mathematics Solutions for Polynomials - Exercise 2.2 in Chapter 2 - Polynomials. Find a quadratic polynomial of √2, 1/3 as the sum and product of its zeroes respectively. Thus, 3x2-3√2x+1 is the quadratic polynomial. What is the quadratic polynomial whose sum and the product of zeroes is √ 2 3 respectively?p(x)=x2−2 x+3. What is the quadratic polynomial whose sum of zeros is by 2 and product of zeros is?⇒ x² - 2x - 8. What is the quadratic equation if the sum of roots is 2 and product of roots is 5?∴x2−2x+5=0 is the quadratic equation. Tải thêm tài liệu liên quan đến nội dung bài viết What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? Clip What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? ?Bạn vừa đọc tài liệu Với Một số hướng dẫn một cách rõ ràng hơn về Review What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? tiên tiến nhất Share Link Cập nhật What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? miễn phíBạn đang tìm một số trong những Share Link Cập nhật What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? Free. Hỏi đáp thắc mắc về What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively?Nếu sau khi đọc nội dung bài viết What is the quadratic polynomial whose sum and product of zeros is root 2 1 by 3 respectively? vẫn chưa hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Ad lý giải và hướng dẫn lại nha #quadratic #polynomial #sum #product #zeros #root - 2022-10-04 14:10:48 What is the quadratic polynomial whose sum and the product of zeroes is √ 2 1 3 respectively?NCERT Solutions Class 10 Mathematics Solutions for Polynomials - Exercise 2.2 in Chapter 2 - Polynomials. Find a quadratic polynomial of √2, 1/3 as the sum and product of its zeroes respectively. Thus, 3x2-3√2x+1 is the quadratic polynomial.
What is the quadratic polynomial whose sum and the product of zeros is root 2 and half respectively?Hence, the required polynomial is 2x² - 2√2x -3.
What is the quadratic polynomial whose sum and the product of zeroes is root 2?f(x) = 0 rArr (x-3sqrt2)(x+2sqrt2) = 0`
` rArr x -3sqrt2 = 0 or x + 2 sqrt2 = 0` ` rArr x = 3 sqrt2 or x =- 2sqrt2. ` Hence, the required polynomial is ` f(x) = x^(2) - sqrt2x - 12` whose zeros are `3sqrt2 and -2sqrt2. What is the quadratic equation if the sum of roots is 2 and product of roots is 5?∴x2−2x+5=0 is the quadratic equation.
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