find a quadratic polynomial each with the given numbers as the sum and product of it's zeroes respectively:
(a) 1/4,-1
(b) √2,1/3
(c) 0,√5
(d) 1,1
(e) -1/4,1/4
(f) 4,1
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find a quadratic polynomial each with the given numbers as the sum and product of it's zeroes respectively:
(a) 1/4,-1
(b) √2,1/3
(c) 0,√5
(d) 1,1
(e) -1/4,1/4
(f) 4,1
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Answers:
We know that,
The standard form of quadratic polynomial,
=> x² - (sum of zeroes)x + (product of zeroes)
a) 1/4, - 1
=> x² - (1/4)x + (-1)
=> x² - (1/4)x - 1
=> 4x² - x - 4
(b) √2,1/3
=> x² - (√2)x + 1/3
=> x² - √2x + 1/3
=> 3x² - 3√2 + 1
(c) 0,√5
=> x² - (0)x + √5
=> x² - ox + √5
=> x² + √5
(d) 1,1
=> x² - (1)x + 1
=> x² - x + 1
(e) -1/4,1/4
=> x² - (-1/4)x + (1)4)
=> x² + 1/4 x + 1/4
=> 4x² + x + 1
(f) 4,1
=> x² - (4)x + 1
=> x² - 4x + 1
Therefore, the required polynomials are:
a) 4x² - x - 4 b) 3x² - 3√2 + 1 c) x² + √5
d) x² - x + 1 e) 4x² + x + 1 f) x² - 4x + 1