Question

Find a quadratic polynomial each with the given numbers as
the sumn and product of its zeroes respectively.
(1) √2,1/3
(ii) 0,√5​

Answer 1

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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) 1/4 , -1 (ii) √2 , 1/3 (iii) 0, √5 (iv) 1,1 (v) -1/4 ,1/4 (vi) 4,1

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Answers

99EkanshNimbalkar

99EkanshNimbalkar Ace

SOLUTION

(i) 1/4 , -1 Let the polynomial be ax2 + bx + c, and its zeroes be α and ß α + ß = 1/4 = -b/a αß = -1 = -4/4 = c/a If a = 4, then b = -1, c = -4 Therefore, the quadratic polynomial is 4x2 - x -4. (ii) √2 , 1/3 Let the polynomial be ax2 + bx + c, and its zeroes be α and ß α + ß = √2 = 3√2/3 = -b/a αß = 1/3 = c/a If a = 3, then b = -3√2, c = 1 Therefore, the quadratic polynomial is 3x2 -3√2x +1. (iii) 0, √5 Let the polynomial be ax2 + bx + c, and its zeroes be α and ß α + ß = 0 = 0/1 = -b/a αß = √5 = √5/1 = c/a If a = 1, then b = 0, c = √5 Therefore, the quadratic polynomial is x2 + √5. (iv) 1, 1 Let the polynomial be ax2 + bx + c, and its zeroes be α and ß α + ß = 1 = 1/1 = -b/a αß = 1 = 1/1 = c/a If a = 1 , then b = -1, c = 1 Therefore, the quadratic polynomial is x2 - x +1. (v) -1/4 ,1/4 Let the polynomial be ax2 + bx + c, and its zeroes be α and ß α + ß = -1/4 = -b/a αß = 1/4 = c/a If a = 4, then b = 1, c = 1 Therefore, the quadratic polynomial is 4x2 + x +1. (vi) 4,1 Let the polynomial be ax2 + bx + c, and its zeroes be α and ß α + ß = 4 = 4/1 = -b/a αß = 1 = 1/1 = c/a If a = 1, then b = -4, c = 1 Therefore, the quadratic polynomial is x2 - 4x +1

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