This GMAT sample question is a problem solving question in Quadratic Equations in Algebra. Concept tested: Relating coefficients of quadratic equations to points on the curve described by the equation - elementary coordinate geometry. A medium difficulty, 650 to 700 level GMAT maths question in algebra.

Question 15 : If the curve described by the equation y = x^{2} + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

- -1
- 4
- 1
- -4
- 0

From INR

y = x^{2} + bx + c is a quadratic equation and the equation represents a parabola.

The curve cuts the y axis at 4.

The x coordinate of the point where it cuts the y axis = 0.

Therefore, (0, 4) is a point on the curve and will satisfy the equation.

Substitute y = 4 and x = 0 in the quadratic equation: 4 = 0^{2} + b(0) + c

Or c = 4.

The product of the roots of a quadratic equation is \\frac{c}{a})

In this question, the product of the roots = \\frac{4}{1}) = 4.

The roots of a quadratic equation are the points where the curve (parabola) cuts the x-axis.

The question states that one of the points where the curve cuts the x-axis is -4.

So, -4 is one of roots of the quadratic equation.

Let the second root of the quadratic equation be r_{2}.

From step 2, we know that the product of the roots of this quadratic equation is 4.

So, -4 * r_{2} = 4

or r_{2} = -1.

The second root is the second point where the curve cuts the x-axis, which is -1.

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