Question

Complete the statements.

Graph ___ has one real root.
Graph___ has a negative discriminant.
Graph __ has an equation with coefficients
a = 1, b = 4, C = -2

Answer 1

First blank -- B

Second blank -- A

Third blank -- C

Explanation:

To find characteristics of a quadratic equation from just looking at the graph is very simple. Here are few points which you can keep in mind which solving these type of questions.

• If value of a (coefficient of
  `x^(2)`) is positive then parabola will open upward and if value of a is negative then parabola will open downward.
• c is the value of y-intercept of the graph.
• The number of times the graph will cut the x-axis is the number of real roots of the equation. If graph touches the x-axis then the number of real roots will remain two but now they are equal so the number of solution will be one (For answering questions you can assume that the roots and solutions are one and the same thing so the answer of first question will be graph B). If it doesn't touch or cut the x-axis ( as in case of graph A ) the number of real roots is equal to zero but still there are two roots of this quadratic equation and now they are imaginary roots. (Number of roots of a quadratic are always two. Either both can be real or both can be imaginary)
• To check which type of roots a quadratic equation has you can check the discriminant of the equation which is (in terms of a, b, c)

`D=b^(2) -4ac`

if D > 0 then two distinct real roots (graph cuts x-axis at two distinct points)

if D = 0 then two equal real roots (graph touches x-axis)

if D < 0 then two imaginary roots (graph doesn't touch x-axis)

For graph A : D < 0 (as it has imaginary roots)

For graph B : D = 0 (as it touches the x-axis)

For graph C : D > 0 (as
`D=b^(2)-4ac=4^(2)-4 * 1 * (-2)=16+8=24`)