Question

find the nature of the roots of the following quadratic equation :- 10x²-7x+13=0​

Answer 1

Question

Find the nature of the roots of the following quadratic equation :-

10x²-7x+13=0

Answer

10x² - 7x + 13 = 0

Let

a = 10

b = -7

c = 13

Discriminant = b² - 4ac

= (-7)² - 4 × 10 × 13

= 49 - 520

= -471

Since the value is negative, therefore the nature of roots is imaginary or not real.

Must Know

b2-4ac = 0 → The roots are real, equal and rational

b2-4ac = 0 → The roots are real, equal and rational

b2 - 4ac > 0 but not a perfect square→The roots are real, distinct and irrational

b2-4ac<0 → The roots are imaginary

b2 - 4ac >/= 0 →The roots are real

Answer 2

${\huge{\underline{\underline{\sf{\maltese\; Question:-}}}}}$

Q) Find the nature of the roots of the following Quadratic Equation :- 10x² - 7x + 13 = 0 .

${\huge{\sf{\underline{\underline{\maltese\;Answer\checkmark}}}}}$

☆ Given :-

• The Quadratic Equation : 10x² - 7x + 13 = 0

☆ To Find :-

• The nature of the roots .

☆ Solution :-

We know that the standard Quadratic Equation is in the form -

$\boxed{ \tt \: a {x}^{2} + bx + c}$

After Comparing it with the given Equation ; we get :

• a = 10
• b = -7
• c = 13

To know the nature of the roots , we have to find it's Discriminant (d)

$\mapsto \rm \: {d} = {b}^{2} - 4ac$

$\mapsto \rm \: d = {( - 7)}^{2} - 4 \times 10 \times 13$

$\mapsto \rm \: d = 49 - 520$

$\mapsto \boxed{ \red{ \rm \: d = - 471}}$

As you can see

$\rm \: d < 0$

$\rm \: as \: the \: discriminant \: is \: less \: than \: 0 \\ \rm \: so \: the \: roots \: are \pink{\: imaginary } \: .$

Roots are Imaginary or Unreal / Not - Real .

_________________________

☆ Know More :-

• If ,

$\rm \: d > 0 \: \: \: roots \: are \: real \:and \: distinct \: .$

• If ,

$\rm \: d = 0 \: \: \: roots \: are \: real \: and \: equal.$

• If ,

$\rm \: d < 0 \: \: \: roots \: are \: imaginary \: .$

• The degree of the Quadratic Polynomial is 2 .

• A Quadratic Polynomial has 2 roots , they maybe distinct or real .

• The roots of a Quadratic Equation can be found by Middle term splitting or using Quadratic Formula .