Question

Find a cubic polynomial whose zeroes are 3,5 and -2.[Don't spam]

Answer 1

Answer: x^3-6x^2-x+16

Step-by-step explanation:x^3-x^2(sum of roots) + x(sum of products of roots taken 2 at a time) - (products of roots ) and substituting all values we will get the required answer

Answer 2

ANSWER:

• x³ - 6x² - x + 30 = 0

GIVEN:

• Zeroes of a cubic polynomial are 3 , 5 and - 2.

TO FIND:

• The cubic polynomial.

EXPLANATION:

3 , 5 and - 2 are the zeroes of the polynomial.

(x - 3)(x - 5)(x + 2) = 0

(x - 3)(x - 5) = x² - 5x - 3x + 15

x² - 5x - 3x + 15(x + 2) = 0

x³ - 5x² - 3x² + 15x + 2x² - 10x - 6x + 30 = 0

x³ - 8x² + 2x² - 16x+ 15x + 30 = 0

x³ - 6x² - x + 30 = 0

Hence the cubic polynomial with zeroes 3 , 5 and - 2 is x³ - 6x² - x + 30 = 0.

VERIFICATION:

x³ - 6x² - x + 30 = 0

•°• Substitute x = 3

•°• 3³ - 6(3)² - 3 + 30 = 0

•°• 27 - 6(9) - 3 + 30 = 0

•°• 24 - 6(9) + 30 = 0

•°• 54 - 54 = 0

•°• 0 = 0

°•° Substitute x = 5

°•° 5³ - 6(5)² - 5 + 30 = 0

°•° 125 + 30 - 6(25) - 5 = 0

°•° 155 - 150 - 5 = 0

°•° 155 - 155 = 0

°•° 0 = 0

•°• Substitute x = - 2

•°• (- 2)³ - 6(- 2)² + 2 + 30 = 0

•°• - 8 - 6(4) + 32 = 0

•°• - 8 - 24 + 32 = 0

•°• 32 - 32 = 0

•°• 0 = 0

HENCE VERIFIED.