Question

If b2-4ac > 0 in ax2 + bx + c=0, then what can you say about roots of the equation

Answer 1

Question:

If b² - 4ac > 0 in ax² + bx + c = 0 , then what can be said about the roots of the equation?

Answer:

The equation will have real and distinct roots.

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.

• 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 .

• 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:

The given quadratic equation is ;

ax² + bx + c = 0.

It is given that,

=> b² - 4ac > 0

=> D > 0

Since,

The discriminant of the quadratic equation is greater than zero , thus its roots will be real and distinct.

Answer 2

Answer:

$\large\boxed{\sf{Real\;and\; distinct\:roots}}$

Step-by-step explanation:

Given a quadratic equation such that,

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

Now, we know that descriminant of a quadratic equation is given by,

• $\large \red{D = {b}^{2} - 4ac}$

Now, According to question,

• ${b}^{2} - 4ac > 0$

That is, we have, D > 0

Now, for a quadratic equation, we know that,

• For D > 0, real and distinct roots
• For D = 0, real and equal roots
• For D < 0, imaginary roots

So, clearly, we can say that, the nature of roots is real and distinct.