Question

find the nature roots of 5x²-2√15x+13=0

Answer 1

Step-by-step explanation:

Given:-

5x^2-2√15x+13=0

To find:-

Find the nature roots of 5x^2-2√15x+13=0 ?

Solution:-

Given quardratic equation is 5x^2-2√15x+13=0

On comparing this with the standard quadratic equation ax^2+bx+c = 0

a = 5

b = -2√15

c = 13

To find the nature of the roots of the above equation then we have to find the value of its discriminant.

We know that

ax^2+bx+c = 0 is a quardratic equation then the discriminant is D = b^2-4ac

=>D = (-2√15)^2-4(5)(13)

=> D = 60-260

=> D = -200 < 0

Since , D<0 the equation has no real roots .i.e. It has imaginary roots.

Answer:-

Nature of the roots :

No real roots.i.e. It has imaginary roots.

Used formulae:-

• The standard quadratic equation is ax^2+bx+c = 0
• ax^2+bx+c = 0 is a quardratic equation then the discriminant is D = b^2-4ac
• Discriminant is used to know the nature of the roots .
• If D>0 ,it has two distinct and real roots.
• If D<0 ,it has no real roots.i.e.imaginary roots.
• If D= 0 ,it has real and equal roots

Answer 2

$5x^{2}-2\sqrt{15} x+13$

Now, we have to find discriminant (D)

If,

D<0 then Complex roots

D>0 then Real and distrinct roots

D=0 then Real and equal roots

$D=b^{2}-4ac$

In the given equation :-

a = 5

b= -2$\sqrt{15}$

c = 13

$D=(-2\sqrt{15}) ^{2}-4(5)(13)\\D=60-260\\D=-200$

Hence, the nature of roots is complex