Question

if one zero of polynomial x^2+5x+k is 5,then the value of k is?​

Answer 1

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k = (-50)

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step-by-step explanation:

Given,

a quadratic equation,

${x}^{2}+5x+k=0$

we know that,

the general form of a quadratic equation is,

$a{x}^{2}+bx+c=0$

so,

comparing the given equation with the general form,

we get,

a = 1

b = 5

c = k

now,

given,

one of the root is 5

so,

let,

the another root be 'm'

now,

we know that,

sum of the roots of a quadratic equation = -b/a

=> 5+m = -b/a

=> 5+m = -5/1

=> 5 + m = -5

=> m = -5 -5

=> m = -10

therefore,

the other root is (-10)

now,

we know that,

product of roots = c/a

=> 5m = k/1

=> 5m = k

=> k = 5m

now,

putting the value of 'm',

we get,

=> k = 5 × (-10)

=> k = -50

Hence,

value of K is(-50)

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