Question

If the sum of the square of the zeroes of the polynomial p(x)= x^2+ + 7x+kis 25, then k
is equal to


​

Answer 1

Given,

A polynomial p(x) = x²+7x+k

Sum of the square of the zeroes = 25

To Find,

The value of k.

Solution,

Since we are given a polynomial function

p(x) = x²+7x+25

Let the zeroes of the polynomial be x and y.

Now,

Sum of zeroes = x+y = -b/a = -7

Product of zeroes = x*y = c/a = k

And it is given that

x²+y² = 25

(x+y)²-2xy = 25

(-7)²- 2k = 25

-2k = 25-49

-2k = -24

k = 12

Hence, the value of k is 12.

Answer 2

Answer:

k=12

Step-by-step explanation:

Let the zeroes be a and b.

Then, $a+b=7$ and $a*b=k$.

Since, $a^{2} + b^{2} =25$

$a^{2} +b^{2} +2ab-2ab=25$

$(a+b)^{2} -2ab=25$

Putting the values,

$7^{2} -2k=25$

$49-2k=25$

$49-25=2k$

$24=2k$

$k=12$