Question

If the zeroes of the polynomial x^3 - 15x^2 + 71x + p are in A.P, find the value of p.

Class X Question

Answer 1

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Answer 2

Given : equation :x³+15x²+71x+p

To find : the value of p

Explanation:

The zeroes of the polynomial are in AP

thus

let the zeroes be a-d , a , a+d

thus

the sum of the roots = a-d+a+a+d = 3a

3a = 15

a = 5

now , a is the root of the equation

so , it will satisfy thus putting x = 5

x³+15x²+71x+p =0

Putting x= 5 we get

(5)³ +15(5)²+71(5) +p =0

125 -375+355+p=0

p = 105

Hence , The value of p is 105

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