Question

A quadratic polynomial if the sum and product of whose zeroes are -3 & 2​

Answer 1

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Answer 2

★ Answer

Sum of zeroes (α + β) = -3

Product of zeroes (αβ) = 2

Now, We know that

Quadratic Polynomial = x² - (Sum)x + Product

So, we get

→ Quadratic polynomial = x² - (-3)x + 2

→ Quadratic polynomial = x² - (-3x) + 2

→ Quadratic polynomial = x² + 3x + 2

$\rule{200}{1}$

★ Factors :

→ x² + 3x + 2 = 0

→ x² + 2x + 1x + 2 = 0

→ x(x + 2) +1(x + 2) = 0

→ (x + 1)(x + 2) = 0

→ x + 1 = 0

→ x = -1

Or

→ x + 2 = 0

→ x = -2

$\rule{200}{1}$

★ Verification :

Sum of zeroes = -b/a = -3/1 = -3

Product of zeroes = c/a = 2/1 = 2

Hence verified