The abcissae of two points A, B are roots of x2 + 4x - 45 = 0. The centre of the circle for which AB are diameter isa)(2, 7/2)b)(4, -7)c)(-2, 7/2)d)(-2, -7/2)Correct answer is option 'C'. Can you explain this answer?

Question

Answer

(x+9)(x-5) = 0
x = 5, -9
(y-3)(y-4) = 0
y = 3, 4
(5,3) (-9,4)
Centre = (-4/2, 7/2)
= (-2, 7/2)

Answer

The correct answer will be (-2,0)
solve the quadratic u will get -9 & 5 as root .
so end points of diameter will be (-9,0) & (5,0)
centre must be the mid point as (-2,0).

Answer

There's probably something which you're missing, because with the given information we can say both C& D are correct.

Answer

I know i have x coordinate as -2 but i think y voordinate should be zero.

Answer

Given:
The equation x^2 + 4x - 45 = 0 has two roots, which are the abcissae (x-coordinates) of two points A and B.

To Find:
The center of the circle for which AB is the diameter.

Solution:
To find the center of the circle, we need to find the midpoint of the line segment AB.

Step 1: Find the roots of the quadratic equation.
The given equation is x^2 + 4x - 45 = 0.
We can solve this equation by factoring or applying the quadratic formula. Let's use the quadratic formula.

The quadratic formula states that for an equation ax^2 + bx + c = 0, the roots are given by:
x = (-b ± √(b^2 - 4ac)) / 2a

For our equation x^2 + 4x - 45 = 0, the coefficients are:
a = 1, b = 4, and c = -45.

Using the quadratic formula, we can find the roots as follows:

x = (-4 ± √(4^2 - 4(1)(-45))) / 2(1)
x = (-4 ± √(16 + 180)) / 2
x = (-4 ± √(196)) / 2
x = (-4 ± 14) / 2

So the roots are x = (-4 + 14)/2 = 5 and x = (-4 - 14)/2 = -9.

Step 2: Find the midpoint of the line segment AB.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
(midpoint_x, midpoint_y) = ((x1 + x2)/2, (y1 + y2)/2)

Since A and B have the same y-coordinate (as they lie on the x-axis), we can ignore the y-coordinate and focus on finding the midpoint_x.

The abcissae of the points A and B are the roots of the equation, so A = (5, 0) and B = (-9, 0).

Using the midpoint formula, we can find the midpoint_x as follows:

midpoint_x = (5 + (-9))/2
midpoint_x = -4/2
midpoint_x = -2

Step 3: Find the center of the circle.
The center of the circle is given by the coordinates (midpoint_x, midpoint_y).

Since the y-coordinate is not given, we can assume it to be the y-coordinate of either A or B, which is 0.

Therefore, the center of the circle for which AB is the diameter is (-2, 0).

Hence, the correct answer is option C, (-2, 7/2).

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