Question

find the nature of roots of equation 2x^2 + 5x +7 = 0.

Answer 1

$\sf{Answer}$

Given Quadratic equation

2x² + 5x + 7

To find :-

Nature of roots

Concept to know:-

Nature of roots can be determined by Discriminant

Discriminant of Quadratic equation is b²-4ac

If D>0 roots are real & distinct

D<0 roots are complex & conjugate

D = 0 roots are real & equal

Solution:-

2x² + 5x + 7 = 0

Here

• a = 2
• b = 5
• c = 7

b² -4ac = Discriminant

D = (5)² - 4 (2) (7)

D = 25 - 56

D = -31

Hence Discriminant is less than

-31 <0

D<0

Hence Discriminant is less than 0

Roots are Imaginary & Conjugate

So, roots of Quadratic equation 2x²+5x+ 7=0 roots are Imaginary and complex

Know more:-

If D >0 & D is perfect square roots are rational& distinct

If D<0 and D is not a perfect square roots are irrational & conjugate

D = 0 roots are real & equal

Answer 2

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find the nature of roots of equation 2x^2 + 5x +7 = 0.

To find:

Roots.

Solution:

• Nature of roots can be determined by Discriminant.
• Discriminant of Quadratic equation is b²-4ac

Concept to know:-

• If D>0 roots are real & distinct
• D<0 roots are complex & conjugate
• D = 0 roots are real & equal.

_________________

Given Equation:

$2x {}^{2} + 5x + 7 = 0$

Using Discriminant formula:

➪b²- 4ac.

here, a= 2

b= 5

c= 7

$d = (5) {}^{2} - 4(2)(7)$

$d = 25 - 56$

$d = \: - 51$

.'.Discriminant is less than

-31 <0

D<0

Hence Discriminant is less than 0

Roots are Imaginary.

Therefore, the roots of this equation are imaginary.

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➪If D >0 & D is perfect square roots are rational.

➪If D<0 and D is not a perfect square roots are irrational .

➪D = 0 roots are real & equal.

$\sf\red{hope\:it\:helps\:you}$