Question

Explain the benefits of evaluating the discriminant of a quadratic equation before attempting to solve it. What does its value signifies?

Answer 1

Dear Student,

Solution:

Benefits of evaluating Discriminate:
➖➖➖➖➖➖➖➖➖➖➖➖➖

Before solving any Quadratic equation if we

first calculate the value of Discriminate,then

we easily found the nature of roots of that

equation.

To find nature of roots, first calculate

Determinant D.

D = 
${b}^{2} - 4ac$


here a,b and c are the coefficient of x^2,x and

constant term respectively, you can find these

values by comparing given equation by

standard Quadratic equation.

Significance:
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1) D = 0; roots are real and equal

and given by
$= \frac{ - b}{2a}$


2) D >0; roots are real and distinct

given by
$= \frac{ - b + \sqrt{d} }{2a} \\ \\ and \: \: = \frac{ - b - \sqrt{d} }{2a}$


3) D <0; No real roots exists

Hope it helps you.

Answer 2

Hi ,

b² - 4ac determines whether the

quadratic equation ax² + bx + c = 0

has real roots or not ,

Therefore , b² - 4ac is called discriminant

of this Quadratic equation .

So, a quadratic equation ax²+bx+c has ,

i ) two distinct real roots ,

if b² - 4ac > 0,

ii ) two equal real roots ,

if b² - 4ac = 0 ,

iii ) no real roots ,

if b² - 4ac < 0

I hope this helps you.

: )