Question

Find a quadratic polynomial whose zeroes are 5 and -4

Answer 1

The quadratic polynomial is 

x² - x (sum of zeroes) + product of zeroes = 0

here, zeroes are 5 and -4

sum = 1 and product = -20

So, polynomial is x² - x - 20 = 0

Answer 2

Answer:

The quadratic polynomial whose zeroes are 5 and -4 = x² - x - 20

Step-by-step explanation:

Given,

The zeros of the quadratic polynomial are 5 and -4

To find,

The equation of the quadratic polynomial

Recall the concepts

If the zeros are given,

The quadratic polynomial is given by

x² - (sum of roots) x + (product of zeros)

Solution:

we have, the zeros of the polynomial is 5 and (-4)

Sum of zeros = 5+ (-4) = 1

Product of zeros = 5 × (-4) = -20

Hence, the required quadratic polynomial is

x² - (sum of roots) x + (product of zeros) = x² - (1) x + (-20)

= x² - x - 20

∴ The quadratic polynomial whose zeroes are 5 and -4 = x² - x - 20

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