Question

What is the condition for which roots of
the o
equation an? +bx+C =0 are real?​

Answer 1

Answer:

If b^2-4ac is greater than 0,it has real roots

Answer 2

Answer:-

For the roots of equⁿ ax² + bx + c to be real , the Discriminant of this equⁿ should be greater than or equal to to 0 . Otherwise if the Discriminant is less than 0 , then the roots will be complex conjugates [ Imaginary numbers ] . Here Discriminant equals to b² - 4ac .

For ex - (i) A quadratic equation x² - x - 6 = 0.

With respect to Standard form ax² + bx + c ,

• b = (-1) .
• a = 1.
• c = (-6) .

So , its Discriminant = b² - 4ac = (-1)²-4×1×(-6) = 1 + 24 = 25 .

Since D > 0 , hence roots are real .

(ii) Let us see another quadratic equⁿ , 2x² - x + 4 = 0.

Here , with the respect to Standard form ax² + bx + c ,

• a = 2
• b = (-1)
• c = 4

So , its Discriminant = b² - 4ac = (-1)² + 4 × 2 × 4 = 1 - 32 = -31 . So , Discriminant here is D < 0 , so roots are complex.

Also have a look at this table :

$\boxed{\begin{tabular}{|c|c|} Conditions &Nature of Roots \\ \cline{1-2} D>0 & Roots are real \\ \cline{1-2} D=0 & Roots are equal \\ \cline{1-2} D<0 & Roots are complex nos. \end{tabular}}$