Question

Find value of p of this quadratic equations x2 +px +16=0 which has equal roots . Find the roots of the equation

Answer 1

when equation has equal root then

b^2-4ac=0

p^2-4*1*16=0

p^2-64=0

p=√64

p=8

so, equation=x^2+8x+16=0

x^2+4x+4x+16=0

(x+4)^2=0

x+4=0

x=-4

Answer 2

The value of p is 8 or -8.

The roots of the equation is 4,-4.

Step-by-step explanation:

Given : The quadratic equations $x^2 +px +16=0$ which has equal roots .

To find : The value of p ?

Solution :

If the quadratic equation $ax^2+bx+c=0$ has equal roots the the discriminant is zero.

i.e. $b^2-4ac=0$

On comparing the equation,

$a=1,b=p,c=16$

Substitute the value,

$(p)^2-4(1)(16)=0$

$p^2=64$

Taking root both side,

$p=\pm 8$

The value of p is 8 or -8.

Solution of quadratic equation is $x=\frac{-b\pm\sqrt{D}}{2a}$

When p=8, $x^2+8x+16=0$

The solution is,

$x=\frac{-(8)\pm\sqrt{0}}{2(1)}$

$x=\frac{-8}{2}$

$x=-4$

When p=-8, $x^2-8x+16=0$

The solution is,

$x=\frac{-(-8)\pm\sqrt{0}}{2(1)}$

$x=\frac{8}{2}$

$x=4$  

The roots of the equation is 4,-4.

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