Share

In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 2x^2+5sqrt3x+6=0 - CBSE Class 10 - Mathematics

ConceptRelationship Between Discriminant and Nature of Roots

Question

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

2x^2+5sqrt3x+6=0

Solution

We have been given, 2x^2+5sqrt3x+6=0

Now we also know that for an equation ax2 + bx + c = 0, the discriminant is given by the following equation:

D = b2 - 4ac

Now, according to the equation given to us, we have,a = 2, b=5sqrt3 and c = 6.

Therefore, the discriminant is given as,

D=(5sqrt3)^2-4(2)(6)

= 75 - 48

= 27

Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation satisfies this condition, hence it has real roots.

Now, the roots of an equation is given by the following equation,

x=(-b+-sqrtD)/(2a)

Therefore, the roots of the equation are given as follows,

x=(-(5sqrt3)+-sqrt27)/(2(2))

=(-5sqrt3+-3sqrt3)/4

Now we solve both cases for the two values of x. So, we have,

x=(-5sqrt3+3sqrt3)/4

=(-sqrt3)/2

Also,

x=(-5sqrt3-3sqrt3)/4

=-2sqrt3

Therefore, the roots of the equation are (-sqrt3)/2 and -2sqrt3.

Is there an error in this question or solution?

APPEARS IN

Solution In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 2x^2+5sqrt3x+6=0 Concept: Relationship Between Discriminant and Nature of Roots.
S