Question

if one root of the equation px^2-(2p+3)x-(p+1)=0 be 3 find p and also the other root ​

Answer 1

Answer:

Step-by-step explanation:

Put x =3

p *3² -(2p + 3)3 - (p+1) = 0

9p - 6p -9 -p -1 = 0

2p -10 = 0

2p = 10

p = 5

Now lets find the other root

one root = 3

let the other root be ∝

product of roots = c/a = -p-1 / p

                    3*∝= -5-1/5

                       ∝=  -6 / 15

Answer 2

Value of p is 5 and other root of equation is -2/5.

Given:

• If one root of $p {x}^{2} - (2p + 3)x - (p + 1) = 0$ is 3.

To find:

• Find p and other root of the quadratic equation.

Solution:

Concept to be used:

• The root must satisfy the equation, from where find the value of p.
• Put value of p in equation and find another root of the equation by factorization.

Step 1:

Find the value of p.

Put x= 3 in the equation.

$p {(3)}^{2} - (2p + 3)(3) - (p + 1) = 0$

or

$9p - 6p - 9 - p - 1 = 0$

or

$2p = 10$

or

$\bf \red{p = 5}$

Thus,

The value of p is 5.

Step 2:

Find the other root of the equation.

$5 {x}^{2} - (2 \times 5 + 3)x - (5+ 1) = 0$

or

$5 {x}^{2} - 13x - 6 = 0$

Factorize the equation.

$5 {x}^{2} - 15x + 2x - 6 = 0$

or

$5x(x - 3) + 2(x - 3) = 0$

or

$(5x + 2)(x - 3) = 0$

or

$5x + 2 = 0$

or

$\bf \red{x = \frac{ - 2}{5}}$

Thus,

Other root of equation is -2/5.

Learn more:

1) If y = -1 is a zero of the polynomial q(y) =4y³+ky²-y-1 then find the value of k.

https://brainly.in/question/16827836

2) Determine the value of m if 3x² + mx + 4 has x = 1 as one of its roots.

https://brainly.in/question/28984714

#SPJ3