Question

determine the nature of roots of 2x2+5x+5​

Answer 1

EXPLANATION.

Nature of  the roots of equation,

⇒ 2x² + 5x + 5.

As we know that,

⇒ D = discriminant  Or b² - 4ac.

⇒ D = (5)² - 4(2)(5).

⇒ D = 25 - 40.

⇒ D = -15.

⇒ D < 0 Roots are imaginary.

                                                                                                                         

MORE INFORMATION.

Conditions for common roots.

Let quadratic equation are a₁x² + b₁x + c₁ = 0  and  a₂x² + b₂x + c₂ = 0.

(1) = If only roots is common.

x = b₁c₂ - b₂c₁/a₁b₂ - a₂b₁.

y = c₁a₂ - c₂a₁/a₁b₂ - a₂b₁.

Nature of the factors of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

Answer:

Solution:-

2x²+5x+5 = 0

D = b²-4ac

here b=5

a=2,c=5

so,

D = 25-40

= -15

so roots will be imaginary.

In this situation:-

• If D>1 - it has 2 different real roots.

• If D=1 - it has 2 equal real roots

• if D<1 - it has imaginary roots

So therefore it has imaginary roots.

Learn more :-

Conditions for common roots:-

• Let quadratic equation are a₁x² + b₁x + c₁ = 0  and  a₂x² + b₂x + c₂ = 0.

• (1) = If only roots is common.

• x = b₁c₂ - b₂c₁/a₁b₂ - a₂b₁.

• y = c₁a₂ - c₂a₁/a₁b₂ - a₂b₁.

Step-by-step explanation:

Hope it helps!