Question

f(x)=x^3+7x^2+mx+n.

Find m and n

Answer 1

Answer:

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Answer 2

Question :

Find the values if m and n. If x + 3 is a factor of f(x) = x³ + 7x² + mx + n and f(x) = 35.

Solution :

» x + 3 is a factor of f(x) = x³ + 7x² + mx + n.

→ x + 3 = 0

→ x = - 3

Put value of x in this .. x³ + 7x² + mx + n

→ f(-3) = (-3)³ + 7(-3)² + m(-3) + n

→ 0 = - 27 + 7(9) - 3m + n

→ 0 = - 27 + 63 - 3m + n

→ 0 = 36 - 3m + n

→ 3m - n = 36 _______ (eq 1)

Now..

f(x) = 35

Let x = 0

→ f(0) = (0)³ + 7(0)² + m(0) + n

→ 35 = 0 + 0 + 0 + n

→ n = 35

Put value of n in (eq 1)

→ 3m - 35 = 36

→ 3m = 36 + 35

→ 3m = 71

→ m = 71/3

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m = 71/3 and n = 35

_______ [ ANSWER ]

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