Question

if one root of the quadratic equationb p^2-3p+k is 5 find value of k​

Answer 1

Answer:

k = -10

Step-by-step explanation:

we can get the value of k by substituting p= 5 in the given equation.

in a quadratic equation p^2-3p+k = 0.

p(x) = p^2-3p+k = 0.

p(5) = 5^2-3(5)+k = 0.

=》25-15+k = 0.

=》10+k = 0.

=》 k = -10.

The first term is,  p^2  its coefficient is  1 .

The middle term is,  -3p  its coefficient is  -3.

The last term, "the constant", is  k = -10 .

Answer 2

Answer:  p = -10

Step-by-step explanation:

Given,

5 is  root  of  polynomial  p² - 3p + k.

It means that if we put the  p = 5 in the above polynomial, According to Remainder theorem Remainder should be zero.

Hence, Putting p = 5

Remainder = 5² - (3×5) + k

0 = 25 - 15 + k

- 10 = k

k = - 10  

Hence,

The value of k is  -10

Now, Let's check:-

Polynomial: p² - 3p - 10

= p² - 3p - 10

= p² + 2p - 5p - 10

= p(p+2) - 5(p + 2)

= (p - 5)(p + 2)

Hence,

p = 5 or  p = -2