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If the Zeros of the Polynomial F(X) = X3 − 12x2 + 39x + K Are in A.P., Find the Value Of K. - CBSE Class 10 - Mathematics

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Question

If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.

Solution

Let a - d, a and a + d be the zeros of the polynomial f(x). Then,

Sum of the zeroes `=("coefficient of "x^2)/("coefficient of "x^3)`

`a-d+a+a+d=(-(-12))/1`

`a-d+a+a+d=12`

`3a=12`

`a=12/3=4`

Since 'a' is a zero of the polynomial f(x).

f(x) = x3 − 12x2 + 39x + k

f(a) = 0

f(a) = 43 − 12(4)2 + 39(4) + k

0 = 64 - 192 + 156 + k

0 = 220 - 192 + k

0 = 28 + k

-28 = k

Hence, the value of k is -28.

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 2: Polynomials
Ex. 2.20 | Q: 6 | Page no. 43
Solution If the Zeros of the Polynomial F(X) = X3 − 12x2 + 39x + K Are in A.P., Find the Value Of K. Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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