Question

If x=3 is the root of the equation x2-x+k=0 find the value of p so that the roots of the quadratic equation x2+k(2x+k+2)+p=0 are equal

Answer 1

Answer: have a look at the picture:

Step-by-step explanation:

Answer 2

The value of p is 12.

Step-by-step explanation:

Given : If x=3 is the root of the equation $x^2-x+k=0$

To find : The value of p so that the roots of the quadratic equation $x^2+k(2x+k+2)+p=0$  are equal ?

Solution :

If x=3 is the root of the equation $x^2-x+k=0$ then it satisfy the equation.

Substitute x=3 in equation $x^2-x+k=0$,

$(3)^2-3+k=0$

$9-3+k=0$

$k=-6$

Substitute in the quadratic equation $x^2+k(2x+k+2)+p=0$,

$x^2+(-6)(2x+(-6)+2)+p=0$

$x^2+(-6)(2x-4)+p=0$

$x^2-12x+24+p=0$

As the roots of the equation are equal so discriminant is zero.

Here, a=1, b=-12 and c=24+p

$D=b^2-4ac=0$

$(-12)^2-4(1)(24+p)=0$

$144-96-4p=0$

$48-4p=0$

$4p=48$

$p=\frac{48}{4}$

$p=12$

Therefore, the value of p is 12.

#Learn more

If a is a root of the equation x2 -(a+b)x + K = 0 find the value of k

https://brainly.in/question/3886713