Find a quadratic polynomial whose sum and product respectively of the zeroes are 2√(3), - 9
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Sum of the zeroes = – 2√3 Show
Product of the zeroes = – 9 P(x) = x2 – (sum of the zeroes) + (product of the zeroes) Then, P(x) = x2 – 2√3x- 9 Using splitting the middle term method, x2 – 2√3x – 9 = 0 x2 – (- √3x + 3√3x) – 9 = 0 x2 + √3x – 3√3x – 9 = 0 x(x + √3) – 3√3(x + √3) = 0 (x + √3)(x – 3√3) = 0 ⇒ x = – √3, 3√3 Sum of the zeroes = – 2√3 Product of the zeroes = – 9 P(x) = x2 – (sum of the zeroes) + (product of the zeroes) Then, P(x) = x2 – (-2√3x) – 9 Using splitting the middle term method, x2 + 2√3x – 9 = 0 x2 + (3√3x – √3x) – 9 = 0 x(x + 3√3) – √3(x + 3√3) = 0 (x – √3)(x + 3√3) = 0 ⇒ x = √3, -3√3
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What is the quadratic polynomial whose sum and product of the zeros are √ 2 and 1 3?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 half respectively?Hence, the required polynomial is 2x² - 2√2x -3.
How do you find a quadratic polynomial with given zeros?How to Find a Quadratic Polynomial if Zeros are Given?. Find the sum.. Find the product.. Substitute the values in the expression x2 - (sum of zeros)x + (product of the zeros) to get the required quadratic polynomial.. |
