Question

Write a quadratic polynomial the sum of whose zero is -3 product is - 10

Answer 1

Given:

• Sum of zeroes = -3
• Product of zeroes = -10

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To find:

• Required Quadratic polynomial.

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Solution:

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Let the zeroes of the polynomial be α and β.

Then,

• Sum of zeroes (α + β) = -3
• Product of zeroes (αβ) = -10

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We know that, standard form of polynomial is

• x² - (α + β)x + (αβ)

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By putting the values

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→ Required polynomial = x² - (-3)x + (-10)

→ Required polynomial = x² + 3x - 10

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Hence,

• The required polynomial is x² + 3x - 10.

Answer 2

Answer:

Given

• Sum of zeroes = -3
• Product of zeroes = -10

To find

• The quadratic polynomial

Solution

Let the quadratic polynomial be

$ax {}^{2} + bx + c$

Sum of zeroes = -b/a

-3 = -b/a

Product of zeroes

-10 = c/a

Calculating the value we get

a = 1, b = 3 and c = -10

So, substituting the value of a, b and c

we get

$ax {}^{2} + bx + c \\ = x {}^{2} + 3x - 10$