Question

The value of p, for which (–4) is a zero of the polynomial x 2 – 2x – (7p + 3) is​

Answer 1

Answer:

Given :-

• (- 4) is a zero of the polynomial x² - 2x - (7p + 3).

To Find :-

• What is the value of p.

Solution :-

Given Equation :

$\bigstar \: \: \sf\bold{\purple{x^2 - 2x - (7p + 3)}}$

$\leadsto$ - 4 is the zero of the given polynomial.

So, according to the question,

$\implies \bf x^2 - 2x - (7p + 3)$

$\implies \sf (- 4)^2 - 2(- 4) - (7p + 3) =\: 0$

$\implies \sf (- 4)(- 4) - (- 8) - (7p + 3) =\: 0$

$\implies \sf 16 + 8 - (7p + 3) =\: 0$

$\implies \sf 24 - 7p - 3 =\: 0$

$\implies \sf - 7p =\: - 24 + 3$

$\implies \sf {\cancel{-}} 7p =\: {\cancel{-}} 21$

$\implies \sf 7p =\: 21$

$\implies \sf p =\: \dfrac{\cancel{21}}{\cancel{7}}$

$\implies \sf p =\: \dfrac{3}{1}$

$\implies \sf\bold{\red{p =\: 3}}$

$\therefore$ The value of p is 3 .

Answer 2

$\bold {solution}$

The value of p is 3 in given polynomial function:

$\bold{x^{2}-2 x-(7 p+3)}$

Given:

$x^{2}-2 x-(7 p+3)$

is a polynomial

Now, we need to find the value of p.

Let, f(x)=

$x^{2}-2 x-(7 p+3)$

Given that x+4 is a factor, applying f(-4) in the above equation, we get f(-4) = 0

Substitute x=-4 in the given equation,

Now we get,f(-4) = (-4)2-2(-4)-(7p+3)

On substituting the above equation, we get,16 + 8 –(7p + 3) = 0

Now, simplifying the above equation,

• 24 = 7p+3

• 7p = 21

• p=3

Hence, the value of p is found to be 3, ∴p = 3