What are the real solution of equation? 2x^2+6x+11=6 ?

2 Answers | Add Yours

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

 To find the real solution of equation? 2x^2+6x+11=6 .

We rewrite the equation by subtracting 6 from both sides.

2x^2+6x+11-6 = 0

2x^2+6x+5 = 0

The discriminant of the equation is (coefficient of x)^2 - 4*(coefficient of x^2)*(constant term) = 6^2-4*2*5 = 36 - 40 = -4 which is negative.

Since the discriminant is negative both roots are not real.

Therefore the the quadratic equation has no real solution as its both roots are not real.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll move all terms to the left side:

2x^2 + 6x + 11 - 6 = 0

We'll combine like terms:

2x^2 + 6x + 5 = 0

Now, we'll verify if the equation has real solutions. For this reason, we'll calculate the discriminant of the equation.

delta = b^2 - 4ac, where ab,c, are the coefficients of the equation:

ax^2 + bx + c = 0

We'll identify a,b,c:

a = 2

b = 6

c = 5

delta = 36 - 40 = -4 < 0

Since delta is negative, then the equation has no real roots, but it has complex roots.

We’ve answered 318,944 questions. We can answer yours, too.

Ask a question