GMAT Maths | Quadratic Equations & Parabola

GMAT Sample Questions | Algebra | Quadratic Equations

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 = x2 + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

  1. -1
  2. 4
  3. 1
  4. -4
  5. 0

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Explanatory Answer

Step 1 of solving this GMAT Quadratic Equations Question : Understand Quadratic Equations - Parabola Theory and compute 'c'

y = x2 + 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 = 02 + b(0) + c
Or c = 4.

Step 2 of solving this GMAT Quadratic Equations Question : Relation between product of roots and 'c'

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.

Step 3 of solving this GMAT Quadratic Equations Question : What do the roots of the quadratic equation represent on the parabola?

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 r2.
From step 2, we know that the product of the roots of this quadratic equation is 4.
So, -4 * r2 = 4
or r2 = -1.

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

The correct choice is (A) and the correct answer is -1.

 

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