How do you form a quadratic polynomial when sum and product of zeros are given?
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Sum of zeroes = α + β =√2 Show
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. Question Open in App Solution Let the zeroes be α and β According to the question:α+β=−3and αβ=2 The quadratic polynomial whose sum and product of the zeroes are given is given by : x²−(α+β)x+αβ ⇒ Then the quadratic polynomial will be : ⇒ x²−(−3)x+2 (adsbygoogle = window.adsbygoogle || []).push({}); ⇒x²+3x+2Hence, the quadratic polynomial is x2+3x+2Suggest Corrections 219 Similar questions Q. Find a quadratic polynomial whose sum and product respectively of the zeros, are −32√5,−12. Q. Find a quadratic polynomial whose sum and product of zeroes are √2 and 3 respectively. Solve Textbooks Question Papers What is the quadratic polynomial whose sum and the product of zero is?The quadratic polynomial whose sum and product of the zeroes are given is given by : x²−(α+β)x+αβ
What is the equation of the quadratic function whose sum and product of the zeros are 5 and 6 respectively?= x² - ( sum of Zeroes ) x + product of zeroes . p(x) = x² - (-5)x + 6. p(x) = x² + 5x +6 . Hence, the quadratic polynomial is x² +5x + 6 .
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