Question

If the sum of roots of the quadratic equation, x² - (p+4) x + 5= 0 is 0, find the value of "p".
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Answer 1

Answer:

p=-4

Step-by-step explanation:

Sum of zeroes:0

We know that,

Sum of zeroes of a quadratic equation = -b/a = -(coefficient of x)/(coefficient of x^2)

Sum of zeroes = -(-(p+4))/1

0 = (p+4)

p+4=0

p = -4

Answer 2

Given:

Given equation is x² - (p+4) x + 5= 0 and the sum of its zeros is 0.

To find:

We have to find the value of p.

Solution:

To determine the value of p we have to follow the below steps as follows-

The given equation is x² - (p+4) x + 5= 0.

Its roots or zeros are given as-

$x = \frac{ p + 4 + \sqrt{ {(p + 4)}^{2} - 4 \times 5} }{2} \\ x = \frac{ p + 4 - \sqrt{ {(p + 4)}^{2} - 4 \times 5} }{2}$

The sum of the two zeros of the equation is 0.

So, we can write-

$\frac{ p + 4 + \sqrt{ {(p + 4)}^{2} - 4 \times 5} }{2} +\frac{ p + 4 - \sqrt{ {(p + 4)}^{2} - 4 \times 5} }{2} = 0 \\ \frac{p + 4 + p + 4 }{2} = 0 \\ \frac{2p + 8}{2} = 0 \\ p + 4 = 0 \\ p = - 4$

Hence the above expression results in the value of p as -4.

Thus, the value of p is -4.