Question

if -2 is a root of the quadratic equation x^2 -px -5=0 and the quadratic equation x^2 +px +k =0 has equal roots find value of k. ( step by step explanation )
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Answer 1

Answer:

first put x = -2 in x^2 -px-5 = 0

you will get the value of p

then put value of p in x^2 +px +k =0

you will get your answer

Answer 2

The value of k is $\frac{1}{16}$.

Step-by-step explanation:

The given quadratic equation is

$x^2-px-5=0$

It is given that -2 is a root of this quadratic equation. It means this equation is true for x=-2.

$(-2)^2-p(-2)-5=0$

$4+2p-5=0$

$2p-1=0$

$2p=1$

$p=\frac{1}{2}$

The value of p is 1/2.

If a quadratic equation $ax^2+bx+c=0$ have equal roots if $b^2-4ac=0$.

The second equation is

$x^2+px+k=0$

Here, a=1, $b=p=\frac{1}{2}$ and c=k.

$(\frac{1}{2})^2-4(1)(k)=0$

$\frac{1}{4}-4k=0$

$\frac{1}{4}=4k$

Divide both sides by 4.

$\frac{1}{16}=k$

Therefore, the value of k is $\frac{1}{16}$.

#Learn more

Find the value of k if the equation x^2-2 (k+1)x+kx=0 has equal roots.

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