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# In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 2x^2-2sqrt2x+1=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^2-2sqrt2x+1=0

#### Solution

We have been given, 2x^2-2sqrt2x+1=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=-2sqrt2 and c = 1.

Therefore, the discriminant is given as,

D=(-2sqrt2)^2-4(2)(1)

= 8 - 8

= 0

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 and equal 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=(-(-2sqrt2)+-sqrt0)/(2(2))

=(2sqrt2)/4

=1/sqrt2

Therefore, the roots of the equation are real and equal and its value is 1/sqrt2

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^2-2sqrt2x+1=0 Concept: Relationship Between Discriminant and Nature of Roots.
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