Question

Find all values of p and q so that 1, -2 are zeros of the polynomial f(x) = x3 + 10x2 +px + q.

Answer 1

1] When x = 1 , [1]³+10[1]²+p+q=0

∴ p+q+2-11→equation 1]

2] When x = -2, [-2]³+10[-2]²- 2×p +q=0

∴ -2+q= -32→equation 2]

From equation 1] and equation 2]→

3×p=21

∴ p = 7

and

7+q = -11

∴ q = -8

Answer 2

Answer:

The value of p = 7 and q = -8.

Step-by-step explanation:

Given:

x³ + 10x² + px + q = 0

1 and -2 are the zeros of the polynomial equation

To find:

the values of p and q

Step 1

Let the polynomial equation be x³ + 10x² + px + q = 0

When x = 1 , then the above equation will be

[1]³ + 10[1]² + p + q = 0

p + q + 2 - 11 ...........(1)

When x = -2,

[-2]³ + 10[-2]² - 2×p + q = 0

-2 + q= -32 ...........(2)

Step 2

Substracting (1) and (2) then we get

3×p = 21

p = 21/ 3

p = 7

and

7+q = -11

q = -8

Therefore, the value of p = 7 and q = -8.

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