Question

write all the values of p for which the quadratic equation x2 + px + 16 =0 zero has equal roots find the roots of the equation is obtained

Answer 1

Answer:

p= 8,-8

Roots = -4,4

Step-by-step explanation:

Given : The quadratic equation $x^2+px+16=0$

To find : Write all the values of p for which the quadratic equation has equal roots find the roots of the equation is obtained?

Solution :

The quadratic equation,

$x^2+px+16=0$

If roots are equal then discriminant is 0.

General form - $ax^2+bx+c=0$

$D=b^2-4ac$  

Equation is $x^2+px+16=0$

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

$b^2-4ac=0$

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

$p^2-64=0$

$p=\sqrt{64}$

$p=\pm 8$

Solution 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.

Answer 2

So this answer is above in Pics

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