If-2x-2-2p-13-x-2-0-is-exactly-divisible-by-x-3-then-the-value-of-p-is-

Question Number 68351 by mhmd last updated on 09/Sep/19

If 2 x^{2} + (2 p - 13) x + 2 = 0 is exactly divisible

by x - 3, then the value of p is

Answered by $@ty@m123 last updated on 09/Sep/19

f (x) = 2 x^{2} + (2 p - 13) x + 2

A T Q,

f (3) = 0

\Rightarrow 2 \times 3^{2} + (2 p - 13) \times 3 + 2 = 0

\Rightarrow 18 + 6 p - 39 + 2 = 0

\Rightarrow 6 p = 39 - 20

\Rightarrow p = \frac{19}{6}

Answered by Rasheed.Sindhi last updated on 10/Sep/19

A n O ther W ay

(2 x^{2} + (2 p - 13) x + 2) \div (x - 3)

By synthetic division :

(\begin{matrix} 3) & 2 & 2 p - 13 & 2 \\ 6 & 6 p - 21 \\ 2 & 2 p - 7 & 6 p - 19 \end{matrix})

As x - 3 is factor

∴ 6 p - 19 = 0 \Rightarrow p = \frac{19}{6}