Question

find the values of m and n so that the polynomial x³-mx²-13x+n has x-1 and x+3 as factors​

Answer 1

Hey mate Here is your answer.

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. Hope it helps you.

Answer 2

Given:

• (x - 1) and (x + 3) are the factors of x² - mx² - 13x + n

Need to find:

• Value of m and n?

Solution:

★ According to the Question:

• (x - 1) and (x + 3) are the factors of x² - mx² - 13x + n

By using Remainder Theorem,

⇒ (x - 1) = 0 and (x + 3) = 0

⇒ x = 1 and x = - 3

⇒ x = 1, - 3

If these are factors of given polynomial,

So, P(1) and P(-3) must be equal to zero.

⇒ P(1) = (1)³ - m(1)² - 13(1) + n = 0

⇒ 1 - 1m - 13 + n = 0

⇒ - 1m - 12 + n = 0

⇒ n - m = 12

⇒ n = 12 + m ....(1)

Also,

⇒ P(-3) = (-3)³ - m(-3)² - 13(-3) + n = 0

⇒ - 27 - 9m + 39 + n = 0

⇒ - 9m + 12 + n = 0

⇒ 9m - n = 12

★ Now, Putting value of n From eq (1),

⇒ 9m - (12 + m) = 12

⇒ 9m - 12 - m = 12

⇒ 8m - 12 = 12

⇒ 8m = 12 + 12

⇒ 8m = 24

⇒ m = 24/8

⇒ m = 3

★ Now, Putting value of m in eq (1),

⇒ n = 12 + 3

⇒ n = 15

∴ Hence, the value of m and n is 3 and 15 respectively.