Question

The graph of the quadratic equation intersects with the x-axis 2 times. This means that there are two solutions and the value of the discriminant is ...
A. 0
B. Positive
C. Negative

Answer 1

Answer:

B. Positive

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree and the graph of the equation will intersect the x-axis same number of times.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Explanation:

It is given that ,

The graph of the given quadratic equation intersect the x-axis two times.

Also,

We know that x-axis is a real number line, thus; we can say that, the quadratic equation in consideration has two real and distinct solutions (roots) .

Also,

We know that, for real and distinct roots of a quadratic equation, its discriminant must be greater than zero , ie ; its discriminant must be positive.

Hence,

The discriminant would be positive.

Answer 2

Answer:

$\large\boxed{\sf{(B)\:Positive}}$

Step-by-step explanation:

Let us assume a general quadratic equation.

$\large \bold{a {x}^{2} + bx + c = 0}$

Now, we know that, any quadratic equation can has atmost 2 roots. These roots can be :

• Both real
• Both imaginary

Now, we know that, the graph of a quadratic equation is a parabola which can intersect the X axis at two points, one point or zero points.

All the three cases are related to a term called descriminant, denoted by D.

Also, $\large\bold{D={b}^{2}-4ac}$

Now, the following 3 cases are possible.

1. D > 0 ( 2 distinct real roots )
2. D = 0 ( 2 equal real roots )
3. D < 0 ( No real roots )

Clearly, there is only one case when there is 2 distinct real roots, that is, the graph of quadratic equation, will intersect X axis at two points when D > 0.

Hence, correct option is (B) Positive