Question

Q.10. Find the cubic polynomial whose zeroes are 5, 3 and -2

Answer 1

Answer: The polynomial is $x^{3} - 6x^{2} -x +30$

Step-by-step explanation: Hope it helps

Answer 2

$\underline\mathfrak{Given:-}$

• zeroes of cubic polynomial is 5, 3 and -2.

$\underline\mathfrak{To \: \: Find:-}$

• Find A cubic polynomial ......?

$\underline\mathfrak{Solutions:-}$

• α + β + γ = -b/a

5 + 3 + (-2) = -b/a

8 - 2 = -b/a

6/1 = -b/a ______(i).

• αβ + βγ + γα = c/a

5 × 3 + 3 × (-2) + (-2) × 5 = c/a

15 - 6 - 10 = c/a

15 - 16 = c/a

-1/1 = c/a _______(ii).

• αβγ = -d/a

5 × 3 × -2 = -d/a

-30/1 = -d/a _______(iii).

Now, from eq. (i), (ii) and (iii), we get :-

• a = 1
• b = -6
• c = -1
• d = 30

A cubic polynomial:-

ax³ + bx² + cx + d

(1)x³ + (-6)x² + (-1)x + 30

x³ - 6x² - x + 30

hence, the cubic polynomial is x³ - 6x² - x + 30.