Question

Find a quadratic polynomial, the sum and the product of whose zeros are 3 and minus 4 by 5
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Answer 1

Answer:

5x² - 15x - 4 = 0

Step-by-step explanation:

given that,

in a quadratic polinomial

sum of zeros = -3

product of zeros = -4/5

and we know that,

quadratic equation when the sum and product of zeroes are given

= x² - sum. of zeros × x + product of zeros

putting the values,

quadratic equation

= x² - 3x - 4/5 = 0

multiplying the equation by 5

we get,

5x² - 15x - 4 = 0

so,

the required quadratic equation

= 5x² - 15x - 4 = 0

Answer 2

Answer:

5x² - 15 - 4 = 0

Step-by-step explanation:

given,

α + β = 3

αβ = -4/5

quadratic polinomial

= x² - (α + β)x + αβ

= x² - 3x - 4/5 = 0

5(x² - 3x - 4/5) = 0

5x² - 15x - 4 = 0

so,

quadratic polinomial =

5x² - 15x - 4 = 0