Question

1. What is the discriminant of the quadratic equation x2 - 25 =0?

2. The floor of a conference hall can be covered completely with tiles. Its length is 10 ft. longer than its width. If the area of the floor is less than 2000 ft2, what are the possible dimensions of the floor? (Assume that the length and width are integers.) Which of the following are the possible dimensions of the conference hall?

A. The length is 40 ft and the width is 50 ft.
B. The length is 51 ft and the width is 30 ft.
C. The length is 50 ft and the width is 40 ft.
D. The length is 40 ft and the width is 30 ft.

3. Which statement is true about the roots of 5x2 - 5x + 1 = 0?

A. The sum of the roots is less than the product of the roots.
B. The sum of the roots is greater than the product of the roots.
C. The sum and product of the roots are equal.
D. The sum and product of roots cannot be compared.

4. In which quadratic equation is the product of the roots equal to 3?

Answer 1

Answer:

x=2+25 wo so tu uigdfuuu

Answer 2

Given:

1. What is the discriminant of the quadratic equation x2 - 25 =0?

2. The floor of a conference hall can be covered completely with tiles. Its length is 10 ft. longer than its width. If the area of the floor is less than 2000 ft2, what are the possible dimensions of the floor? (Assume that the length and width are integers.) Which of the following are the possible dimensions of the conference hall?

3. Which statement is true about the roots of 5x2 - 5x + 1 = 0?

To Find:

1. Find the value

2. A. The length is 40 ft and the width is 50 ft.

B. The length is 51 ft and the width is 30 ft.

C. The length is 50 ft and the width is 40 ft.

D. The length is 40 ft and the width is 30 ft.

3. A. The sum of the roots is less than the product of the roots.

B. The sum of the roots is greater than the product of the roots.

C. The sum and product of the roots are equal.

D. The sum and product of roots cannot be compared.

Solution:

(1) The value of the discriminant can be found for a quadratic equation as ax2+bx+c=0 using a formula that is,

$D^2=b^2-4ac$

Now apply the values from the equation into the formula, we get

$D^2=0^2+4*1*25\\=100$

Hence, the value of the discriminant is 100.

(2) Let the width of the floor be x then the length will be (x+10), now put in the area formula and the rest values accordingly,

$A=x(x+10)\\x^2+10x<2000\\x^2+10x-2000<0$

Solving the equation using the quadratic formula we get,

$x=\frac{-10\pm \sqrt{100+8000} }{2}\\=-50,40$

So the value of x lies between -50 and 40, now we go through options to see the possible values, we know that x that is width needs to be less than 40 which goes for options b and d and then the difference between length and width is 10 so option d is right

Hence, the correct option is (D).

(3) Let's find the roots of the given equation first by using the quadratic formula,

$x=\frac{5\pm \sqrt{25-20} }{10}\\=\frac{5\pm \sqrt{5} }{10}$

Now finding the sum and the product of the roots, we get

$Sum=\frac{5+\sqrt{5} }{10} +\frac{5-\sqrt{5} }{10} \\=1\\Product=(\frac{5+\sqrt{5} }{10})(\frac{5-\sqrt{5} }{10} )\\=0.2$

so it is observed that sum is greater than product

Hence, the correct option is (B).