Question

Find the nature of quadratic equation x2 + 4x + 7 = 0​

Answer 1

Answer:

We can find the nature of roots of quadratic equations using:-

D=b^2+4ac

in this equation, b=4,a=1,c=7

D=(4)^2-4×7

D=16-28

D= -12

As,D<0

=>This equation has no real solutions.

Hoping this helps you...

Answer 2

Roots of x²+4x+7=0  are imaginary ( not real ) and different

Given:

• Quadratic Equation
• x² + 4x + 7 = 0

To Find:

• Nature of Roots

Solution:

Quadratic equation is of the form ax²+bx+c=0  where a  , b and c are real also  a≠0.

D =  b²-4ac is called discriminant.

D > 0 roots are real and distinct

D = 0 roots are real and equal

D < 0 roots are imaginary ( not real ) and different

Step 1:

Compare  x²+4x+7=0  with ax²+bx+c=0

a = 1

b =4

c = 7

Step 2:

Substitute values of a, b and c and calculate discriminant

D = b²-4ac

D = (4)² - 4(1)(7)

D = 16 - 28

D = -12

Step 3:

Check that -12 < 0 hence D < 0

so roots are imaginary ( not real ) and different