Question

if one zero of quadratic polynomial x²+3x+kis2 ,then find the value of k​

Answer 1

Answer:

The value of k = -10 .

Step-by-step explanation:

If one zero of quadratic polynomial x²+3x+k is 2 , then 2 must satisfy the quadratic equation.

$x^{2} + 3x + k = 0 \\ x = 2, \\2^{2} +3(2)+ k = 0\\4 + 6 + k = 0\\k= -10$

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Answer 2

Answer:

The value of k = -10

Step-by-step explanation:

Given one zero of the polynomial x²+3x+k is 2

To find,

The value of 'k'

Recall the concepts

If 'a' is a zero of the polynomial p(x), then x-a is a factor of p(x)

Factor theorem,

If x-a is a factor of the polynomial p(x), then p(a) = 0

Solution:

Let p(x) = x²+3x+k

Given that 2 is a zero of the quadratic polynomial p(x) = x²+3x+k.

Then we have (x-2) is a factor of the polynomial p(x) = x²+3x+k

By factor theorem p(2) = 0

p(2) = 0 ⇒2²+3x2+k = 0

⇒4+ 6+ k = 0

⇒10+k = 0

⇒k = -10

∴The value of k = -10

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