Question

Nature of quadratic equation 2x^2+2x+2=0 is a)​

Answer 1

Answer:

Given :-

• 2x² + 2x + 2 = 0

To Find :-

• What is the nature of roots of the quadratic equation.

Formula Used :-

$\clubsuit$ Discriminant Formula :

$\mapsto \sf\boxed{\bold{\pink{Discriminant\: (D) =\: b^2 - 4ac}}}$

Solution :-

Given Equation :

$\implies \sf \bold{\purple{2x^2 + 2x + 2 =\: 0}}$

where,

• a = 2
• b = 2
• c = 2

According to the question by using the formula we get,

$\longrightarrow \sf Discriminant\: (D) =\: (2)^2 - 4(2)(2)$

$\longrightarrow \sf Discriminant\: (D) =\: 2 \times 2 - 4 \times 2 \times 2$

$\longrightarrow \sf Discriminant\: (D) =\: 4 - 4 \times 4$

$\longrightarrow \sf Discriminant\: (D) =\: 4 - 16$

$\longrightarrow \sf Discriminant\: (D) =\: - 12$

$\longrightarrow \sf\bold{\red{Discriminant\: (D) =\: - 12 < 0}}$

$\therefore$ The nature of roots of the quadratic equation is real, irrational and distinct.

Hence, the correct options is option no (a) Real, irrational and distinct.

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EXTRA INFORMATION :-

❒ Nature of Roots :

✪ b² - 4ac is the discriminate of the quadratic equation :

◘ b² - 4ac = 0, then the roots are real & equal.

◘ b² - 4ac > 0, then the roots are real & unequal.

◘ b² - 4ac < 0, then the roots are imaginary & no real roots.

Answer 2

The natural of roots of the quadratic equation

2x² + 2x + 2 = 0 are ;

Formula Used :-

$\begin{gathered} \sf\boxed{\bold{\pink{Discriminant\: (D) =\: b^2 - 4ac}}}\\\end{gathered}$

where,

a = 2

b = 2

c = 2

$(D) =\: (2)^2 - 4(2)(2)$

$(D) =\: 2 \times 2 - 4$

$(D) =\: 4 - 4 \times 4$

$(D) =\: 4 - 16$

$(D) =\: - 12$

12 < 0

∴ The nature of roots of the quadratic equation is real, irrational and distinct.

• Option a) is correct

• Real, irrational and distinct.