Question

the value of p for which X + p is a factor X square + px + 3 - p is​

Answer 1

To find, the value of p = ?

(x + p) is a factor of P(x).

∴ x + p = 0

⇒ x = - p

∴ P(x):x^2+px+(3-p)=0

x^2+px+(3-p)=0 ...... (1)

Put x = = - p in (1),

we get

(-p)^2+p(-p)+3-p=0

⇒ p^2-p^{2} +3-p=0

⇒ 3-p=0

⇒ p = 3

Hence, the value of "p is equal to 3".

hope u understood ;)

Answer 2

${x}^{2} + px + 3 - p$

If (x+p) is a factor of the given polynomial.

then, x+p=0 =>x=-p is a zero of the polynomial.

i.e.

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

therefore,p=3(ans)

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