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Zeroes of a Polynomial

If x+2 and x-...

Question

If (x+2) and (x-1) are factors of the polynomial $p (x) = x^{3} + 10 x^{2} + m x + n$ then
(a) $m = 5, n = - 3$
(b) $m = 7, n = - 18$
(c) $m = 17, n = - 8$
(d) $m = 23, n = - 19$

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Solution

ANSWER:
(b) m = 7, n = −18
Let:
px=x3+10x2+mx+n
Now,
x+2=0⇒x=-2
(x + 2) is a factor of p(x).
So, we have p(-2)=0
⇒-23+10×-22+m×-2+n=0⇒-8+40-2m+n=0⇒32-2m+n=0⇒2m-n=32 ...i
Now,

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Similar questions

Q. If (x + 2) and (x − 1) are factors of (x³ + 10x² + mx + n), then
(a) m = 5, n = −3
(b) m = 7, n = −18
(c) m = 17, n = −8
(d) m = 23, n = −19

Q. If x + 2 and x − 1 are the factors of x³ + 10x² + mx + n, then the values of m and n are respectively

(a) 5 and −3

(b) 17 and −8

(c) 7 and −18

(d) 23 and −19

Q. If x+2 and x-1 are factors of

x^{3} + 10 x^{2} + m x + n

then which of the following are the values of m and n respectively?

Q. If (x – 1) and (x + 2) are two factors of the polynomial

2 x^{3} + m x^{2} - x - n

, then the value of

(m^{2} - n^{2})

x - 2

x - \frac{1}{2}

both are the factors of the polynomial

n x^{2} - 5 x + m

m = n = 2

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