Please answer all questions and you will get brainliest:

For what real values of $c$ is $x^2 - 8x + c$ the square of a binomial?

For what real values of $s$ is $x^2 + sx + 144$ the square of a binomial?

For what real values of $c$ is $4x^2 + 14x + c$ the square of a binomial?

Question 1

We want to find real values of c, for which

is the square of a binomial.

If the above quadratic equation is the square of a binomial, then its discriminant is zero.

This implies that:

where a=1, and b=-8

We substitute the values into the formula:

Question 2

We want to find the value of s for which

is the square of a binomial.

In this case too the discriminant must be zero.

D=b² -4ac=0

We put a=1,b=s, and c=144 to obtain:

Question 3

We want to find the value of c, for which

Again we have:

We put a=4 and b=14

4th option is correct xy=-10

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